{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Kenel Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.kernel import (\n",
    "    PolynomialKernel,\n",
    "    RBF,\n",
    "    GaussianProcessClassifier,\n",
    "    GaussianProcessRegressor\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_toy_data(func, n=10, std=1., domain=[0., 1.]):\n",
    "    x = np.linspace(domain[0], domain[1], n)\n",
    "    t = func(x) + np.random.normal(scale=std, size=n)\n",
    "    return x, t\n",
    "\n",
    "def sinusoidal(x):\n",
    "        return np.sin(2 * np.pi * x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 Dual Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3PvmBma+7kXT8ZKuDglKxlBaGkA4eBC8vxmW7Qvls5amWq5rdiVQ0kjlZZo51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\nBklSx2CQJHV+AaEoHQeXC3B0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173d6780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=10, std=0.1)\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=PolynomialKernel(3, 1.), beta=int(1e10))\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y = model.predict(x)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4 Gaussian Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.2 Gaussian processes for regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PHQdJSZz70mL6tz6KW5bfR2ZJtnQPE5oVLUcAvvwC5rzLawMT+POg1kw9ulKl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\nICKio9IAIiI66i/kbWASmhdF2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173df748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 15.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr\")\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### 6.4.3 Learning the hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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kVq5cmenxCSHSz6pbmXtgLpVnVWbRkUW8Wu1ZznXdwku1nsXWlM7ql9hY+GoW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WkAv6b9zoVrhtOnUXe+GPAeFuXFcy6/ACIbQP2wyo9xEp7uweRJLYQQdVjX6K4su2oZu27bxeXt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173df2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data(sinusoidal, n=7, std=0.1, domain=[0., 0.7])\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "model.fit(x_train, y_train, iter_max=100)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", color=\"blue\", label=\"training\")\n",
    "plt.plot(x, sinusoidal(x), color=\"g\", label=\"sin$(2\\pi x)$\")\n",
    "plt.plot(x, y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x, y - y_std, y + y_std, alpha=0.5, color=\"pink\", label=\"std\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4.4 Automatic relevance determination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_toy_data_3d(func, n=10, std=1.):\n",
    "    x0 = np.linspace(0, 1, n)\n",
    "    x1 = x0 + np.random.normal(scale=std, size=n)\n",
    "    x2 = np.random.normal(scale=std, size=n)\n",
    "    t = func(x0) + np.random.normal(scale=std, size=n)\n",
    "    return np.vstack((x0, x1, x2)).T, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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52NiyvjohRL6KsHqGp8XExPCvf/2LcePGYbPZ+PnnnxkzZkzm6/Pnz6dz586sW7eOoKAg\ngoKCSv0ahRDiepCUpOKt99+He+9Vz82ZA716wd9/wzXYpkOIknGDxzO6rvPggw8SHh7O008/ne92\nBw8epF69emiaxrZt2zCbzZnJmrNnz1KlShWOHTvGokWL2LhxY4HnLOhYOS1YsIA+ffpk6+F47Ngx\nBgwYwKxZs64oQVWYWrVqMW3aNMaNG4eu66xevZonn3wSgH79+rFy5crMJtyePG9pk0qjnOx2lThx\nODx7XIdDTU8zGdW0r6uRYQE0lTjydEWUzVkFpWmq6shu9+zxS9jRo7B5M0yapBJGoEa8XngBPv20\nTC9NCHENio6Opm/fvjRv3pyePXvSrFmzbIGUr68vLVu25OGHH2b69OlXfb4hQ4bQtm1b/vrrL2rW\nrJl5zKlTpzJ16tRC9+/QoQN33303v//+OzVr1uSXX34BYPz48fz444+F7h8WFsbTTz/Nl19+Sc2a\nNYmPjwdg9OjRxMXFFbjv6dOnqVmzJu+99x6vvfYaNWvW5PLlywD06tWLkydPFnp+IYQHFDf2s1hL\ndDGWb7+FDh1gyBAVRmoaDB0KbdrAggUldlohBKUbz6xfv55Zs2bxxx9/ZC5vv3TpUiB7PLNw4UKa\nNm1KREQE//73v5k/f35mhdPAgQNp3Lgxd955Jx9//DEVKhRcCFHQsXLGIPPmzcucjufy6quvkpiY\nyKOPPkpERESReihNmTKFmjVrkpCQQPPmzTOnu8XFxWU+HjRoEPXq1aNZs2a0aNGCFi1aZE4NHDt2\nLAsXLqRZs2aMGzeOL774otBzXm2cV1I0/RpeySsqKkovLIj1uORUtcJZ3Zrg6+O545otcOQEeBnV\nXbTuLcU/1oUkOHtBPQ6r4dm+RqfOQ3KKaoBttkCtauBXvJV2ysKmTfDvf0PO/2x++w1eew1WrSqT\nyxJC5GPfvn2ZDQPLSkpKCgEBAaSlpREbG8vnn39OZGQknTp1YtKkSUUKLFxWrVrFpEmT8lyi9mYy\ncuRI+vTpw6BBg7I9n9e/t6ZpW3VdL/qHLEpcmcRfouhS01SzRq8rmDBgtqgYN7Ac+JRMo8eJEyE9\nHd54I/vzzz0HwRV0xj1jA6NRVbMLcYOReEZcC44ePUqfPn0yG51ndTUxmPzWzslWQpVGFqv6bjCo\nRthXk6xLTXffcD09hcxmdXcs1FGNu68jTZrA4cPqK6tFiyAmpmyuSQhxbRszZgwRERFERkYycODA\nzGVki8Pb25s9e/bQq1cvD17h9WXo0KGsXr06W1m4EMJDdF0lgFxxZVHY7CrRZDKqVglXO2DsyDtO\nbtcOfvzRXbQOYDU72LTWTI92yWoRl5S0Eq12EuJmJvHMzW3t2rXceeedhISEePzY0tMoJ5tN3czs\nHk4apZvVqmSapo5vs1/ZCJGLrqsbvpdJPU5LhwoenCRutanEFoBBg4wMCArw3PFLWEAAvPwydOsG\nEyaoPkbz58PSpaoKSQghcpozZ06ez68qRmliu3btOHr06NVd0HVu9uzZZX0JQty47HbnoJ4V/H0L\nX5rM4VAVRgZnhY/Fpva90mojXVcxcoYzYaVpEOgPXl6Zm9x+O4SFqb5G//e0Ax+sLFmYQedoiIgw\ngNFb7ZueAf6y+qQQnibxzM2tQ4cO7N69u0SOLUmjnKw2ldzxeNIoQ5Xkgjq+1Va8pJHFqoIFTVMj\nRmnOESNPrGfqSkgd+AsiWqrk0XW4gtoTT0C9evDZZ3DmDHTsCBs2QGhoWV+ZEEIIIcRVsNpVzOdw\nqFjVVMAy1bquKox03b2dyRnbeXsVHju6BjmtVtWX06GrAUXXwOXlVNXKwZm80jRYtMDBNzOsLJuT\ngcEI0W2NDByoobku08ukzu/lVbw4WAghRKmT39Y52ewqWeLJBtC6rkZmvJ0ft45KGhWH2eIu69U0\nNepT3KqlvK5z6c/w3NOwYiXUq6+CBE8lpUpRnz7qSwghhBDihmG2qIohm13FgAUljdIyVGWRt7sa\nCINBDUBaczzvYrer1yxWdQ5XDGgygilLLKhp4KWp67HaIMAPbHa80zIYdS8wzJh37Og6VnKqqpQ3\nSKcMIYS41slv6pxszulZhSV1rqTnkdUG6PDSf2Hye6rSyFLMFdRSM9QoD7hvxle7GpuL3Q7Hj6nH\ncVvcU+mKm+ASQgghhBCe4XCoWM1gUNXrBcWSFqvqe5nXoKIxS6V6VjYbJKWo3pkOZ3WSt7MiKL8E\nkJcJ0N37GY35b+9iMKhYOLWI/Y1cA6TSC0kIIcqER5JGmqbN0DTtrKZpudt0q9c1TdOmaJp2UNO0\nXZqmFb8rV0mzOdwjOAU5cbboyRSLs6R38SJYvkzdLDOKkejRdeeN3AHbt6nnNE1NKfMEmwNOn1aP\nXceHvJstOhyFf0Z5kRu+EEII4RE3VPwlCpc17jI6F1bJaxBT11VSyJhPtY/RWVGftWO1xaoaVRsN\nKlFkNBS9ytzoTC55e7kHNgtjMqkqqMLiYVciKykFLiVDSqozri7C4G1RtxNCCFEgT1UafQn0KOD1\nnkAD59cY4FMPndezXKtBGApJGrlWrihq0shsgSOHITVVfQc17etKuW7w386FAX3VEmFGg6o+8gS7\nHc7kkTTKq5Lp7AU4d+HKz3Hmglo5QwghrgGXLl3ik08+ueL9evXqxaVLlwrcZvz48fz222/FvTQh\niuJLboT4SxRN1sVKXPKKV+3OlYALWto+a7WR2aKmixmNpTtdzMukFnTJr2Le4YDkNGdSyuROlCWn\nqq+CBiJtzu0uJatzeLLthBDXIIlnREnyyJ1B1/U1QEEZhLuAr3VlI1BB07Rqnji3Rzkc8NUMWPJT\nwTcXh0PduIuaNEozw7696rHZDKdPquTPlY5+uEZjNm1U37dsUjdQs9kzIylZk0YH/obLSer4aTmS\nUhkWuHgZUtKvrHIoPQMSL0rSSAhRbA4HJCRAcrJnjpdfkGWzFfz7fenSpVSoUKHAbV599VXuuOOO\nq7o+IQpyw8Rfwi09n5hO11XlTNZEkMGQ9xS1dHPhFT+uqvq0DBWXeZlKv7+Qa3pbSlruxFHWJt6u\n9+zqh+TtparjC4rVLRb39hkWuJSiqpQkeSSuIWfOQGKiZ44l8YwoSaXVCLsGcDzLzwnO506V0vmL\nxu6AWV+qddp79C54O4ejaH2JdF0tWx+fpXL88CGoXFXdrL2v4AbtmoYWt8X9/Z4h6rHZCn4+RT9W\nXqw29dsrLAyOHoWdOyGmvbrZuhoh6jqcTXSXNufXSDEnXYfTiWq0KDW9WJeXYcvgdMppTiaf5HTK\naVIsKdgcNqx2K1aHFYfuINA7kAq+FQjyDSLIJ4jQgFCqB1bHoEn7LiGud99/D888o4o209Ph7rth\n8mQoV674xxw7diyHDh0iIiICLy8vfH19CQ4OZv/+/fz999/069eP48ePk5GRwRNPPMGYMWMACAsL\nIy4ujpSUFHr27En79u35888/qVGjBj/88AN+fn6MHDmSPn36MGjQIMLCwhgxYgQ//fQTVquV7777\njltvvZVz585x3333cfLkSdq2bcuKFSvYunUrISEhHvrUxE3u+oi/hKLrqipGd+Rekt5VDZ+18bXR\noKZ4ZV2wxG5Xz3kV0CA7c3+jcyW1gnsQ6bpOsiWZU6mnOZlyirPp58iwmbE6VPxltVsxGoyU9y5P\nBZ8ggnzKU8GnAjUDqlPRr2LB1+BK7KSkq6SVqwdTeh5NvLMyoBJNpjz+lHEtQGMyuhNTuu78rDIg\n8CpuGkJ4wK5d8PDDsG+f+t/6ttvUqs916hT/mBLPiJJ0za2epmnaGFQJNbVq1Srdk9vscP4cBAWp\nm4trqlpOdrtaAS2jCFPMXCXCe3ZD7drwzz8qadQmpugJF5fUdDiRAGfPqJtk3Gb1vI5qdni1SaPL\nyXDpItxzL3w+FbZvhfYdwG5zL+uamq6+fL1VospsKdp7SEpRFVE+zv1s9nxX/LiQfoFdZ3ax+8xu\n9f3sbv5O/JuLGReL9bZ8Tb7UDa5L/Yr1qR9cn5bVWtKmZhvqBddDu85WhRPiZrVxIzz6KMyfDx06\nwMWL8J//wEMPwZw5xT/uW2+9xZ49e9ixYwerVq2id+/e7NmzhzrOyG3GjBlUrFiR9PR0oqOjGThw\nIJUqVcp2jAMHDjB37lymTZvG4MGDWbhwIcOGDct1rpCQELZt28Ynn3zCpEmT+OKLL3jllVe4/fbb\nGTduHMuXL2f69OnFfzNCXIUyjb+EYndWGGU44yVjljjJakN1j85C0wBdxZqu5InZojbLGd8sWwoH\nDsDjT7ifMxqyVS7pus7x5AR2nd/D7vN72XVOfT+S9A9ptuJViQf7BFOvQh3qVahDwwr1ia7aituq\nRVHFv4p7I4NB/UWSnAKBASr+Ts+niXfmtRtVHO6XR6xuzZFIA3dyytXnSFZtE2Xk4kXo3h1eew1G\njFD/+06eDN26QXw8eF3Bn4ZZSTwjSlJpJY1OALdk+bmm87lcdF3/HPgcICoqqnS7Jl+8qBIbiefV\nz/kmjRyq7LcolUYW5zS0+L3QfyD8uBgOHXKuSmYF/Ao9ROa1mC2wPU793G8ALPgWzp2FCsFqZCq4\nfNGOlZ+EBPW9QUP1tX2buslqqJusQYMziWr0StPUV2p64SM2NruqTvLyyrbi29EEP86ehZr1L7Hl\n7GpWHl3JH0f+YPfZ3Zm7VvSrSPPQ5tzT5B5qlK9BtYBqVA+sTrXAagR4B+Bl8MLL6IWXwQtN00g2\nJ5NkTiIpI4kkcxInk09y8MJBDl08xMELB1lxaAXpNlXpVMmvEq1rtCbmlhh6NehFRNUISSIJcY36\n8EN44QWIjVU/V6wIn38OtWrByZNQvbpnztO6devMAAtgypQpfP/99wAcP36cAwcO5Aqy6tSpQ0RE\nBACtWrXi6NGjeR57wIABmdssWrQIgHXr1mUev0ePHgQHB3vmjQihXB/xl1AcDneclG6GAH/3axYb\nGPOKUTTV58dkUvu7Kmyyit8LI+5Xle8tW+KIic0MRb2qHGP1iTX8cWw1K4+vISHF/Z9H7fK1aB7S\nlK61b6d6uWpUK1eVWwxB1P99B9ae3TFWrqLiMIMJu24nyXxZfVmSuJhxiROJR7l0YBeWv//G+59V\nXEhfRN/WOmhQJyiMNlWjia0ZQ++6PbglsKY66eVUFXea8mninfm2s8SnvjkGTTPMefdzcsWuee0j\nRCmZMwc6dYIHH1Q/m0zw3HOwZAn8/DP07++Z80g8IzyptJJGPwKPaZo2D7gNSNJ1/dorjT7l7Odz\n4QJq5MaR9ydkt4NmUH2Jco5k5GS2wD9HISUFmjVXFUeHD6n982v8l99xALZsVpVQQ4aqpFHcFuje\nUzXDLuxaCnPCGSiEVoWIlvDLMnVMHXWDtTibf/t6q+1clUeFnTfxklo9zjkVLz0Dxo09zPT9K9DD\nvyM1eCMYHPiafIm5JYbXOr9GVPUomoU2o1pAtStK5IT4F1wCaXfY2XtuL5sSNrExYSObTmxi2cFl\nvLjyRaoHVqd3g970btCbrvW64u/lX+CxhBCl559/wFlJnalcOTWbNiHBc0mjclnmuq1atYrffvuN\nDRs24O/vT6dOncjIyL3wgI+P+48Po9FIenreU3Bd2xmNxkJ7DAjhIddH/CUUq00lQoxGFff5equ/\nKHVdxZx5VWgbnfGkn497tduscVNaGowcAeXLQ6VKpD81jj63fsixyos5FfIDqX6HAAjxq0TnW2KJ\nrRFDyyotaBrSmCCfoOzn2rhB/SI+egTe/QzefQ/69c88XxX/Kipx9f0ieOdtNfcmR+/LB+7/gN9C\nU9l4ajOrE9Yx96/v4HdoHtKU3nV70CesO22qRmMoSiWQ0bkasY939ul5BVXyu/aRpJEoI8eOQfPm\nuZ9v3lzFOp4i8YzwJI8kjTRNmwt0AkI0TUsAXga8AHRdnwosBXoBB4E04AFPnNfjTjnjKKtVdVnN\nr7m066auo6poCiqfTc/Sz6hpM6hXH9asVqNFV7KCWoZFnS9uC7SKVsfy9VU/9+wNDtuVT3fLStfd\nSaNq1SCyFXw7D44cgZq3OKelpWV/rwbNPdUsv88gw6yaZvt4cTb9PHOOLGbq1h/5K2QbtIcWoS1o\nX/lFFr5jOiltAAAgAElEQVRzO9MmtKFPj5K9iRsNRpqHNqd5aHMeavUQAGdSzrDs4DJ+/vtn5u2Z\nx7Rt0wj0DmRwk8GMaDGC9rXaSwWSEGUsOhqWLoWOHd3PHT+ufkXdemvxjxsYGEhyPl21k5KSCA4O\nxt/fn/3797Nx48binygfMTExfPvttzz//PP8+uuvXLxYvGm44uZ0w8RfQnGtjqZpzoVI0tV0LZuz\nLUJesYjB2dfIblfVSTkrbMY9D/v3c+SrKazfsYxh7y/jlvBYVtcy0qVWJxra/8WWubH88lVjgsrn\nk6gxm+HNN+CD91V55+dfwKefqOqlO++Ed9+H0FD4/Xd45WXVE7NJE3h+LNSpC3XCVHlo62gitp0k\n4qXxgJoOt+/CfpYc/oUlR5bz9pb3eXPzJGqXr8X94UO4v/F91A+ul//nlfW9Z5ueV0DMZjCo5Jrd\nnn36nxClJCoKpkyBsWPd/6nabPDLLzBzZvGPK/GMKEkeSRrpuj6kkNd14N+eOFeJOpVl8C0x0T23\nPCerXSVMdF3d4AtMGplh7x7w8VFTvurWVRVCqamgX0EiIjUdki6qKqW7B4O3t6oGcjXFhqL3F8qL\nrrvff2hVaBmpHm/fqnoxpThXsMjauDvLVLM8PwNdRz99nrXnN/PpobksPLYUq8NKdVtjJkY8w+CO\no2kY0giAlpdg5jToU9DCwSUkNCCUkREjGRkxEovdwuqjq5m9ezbz9sxj+vbp1A2uy4gWIxjTagxV\nA6qW/gUKIXjqKdUoslw5GDxYzfIdOxb+7//UAHpxVapUiZiYGJo2bYqfnx+hoaGZr/Xo0YOpU6cS\nHh5Oo0aNaNOmjQfeSXYvv/wyQ4YMYdasWbRt25aqVasSGBjo8fOIG9MNE38Jdy9NVzWR0dl/x5Xg\nKChk1HCuuqZnq0ayLvgWr5kz+aZHdYYfeRxDeQNNqpfn43Ua776/gUohqnfVuO3w2woY2CkRlvys\ndvb2URU8oKqG9uyBESPhjTchMBAGDYKPPoTXX4PWUXBruKpEql1bJZXuvjt3Uua22+DXX8CZNNI0\njcaVwmlcKZxno5/kYsZFlhz+hVn75vLapreZuOl/xFRrw6hm93PfrYPxNfnmfu8G1MBqgLMiy2zN\nt2em+/NyTlHzk6SRKH39+sE776h+Rk8+6czJvgkNGkC7dsU/rsQzoiRp+pUsmV7KoqKi9Li4uNI7\n4SsTYYK6kTH7W+jTE8oH5N7u+Cl1g7I7oHrlvLcB9fqBf2DEEDW16/uf4Nfl8K/R6vGtTaBB7bzn\nXWel63DgGPz+Kzw6BhYshlZRMOltmPox7NoHRhNUKA+hlQo+Vn4sVnjwIfhhkTqewwERTaBvP5j4\nBqQ5G23nXMLVbFG9lKpkP2+6NZ2Zmz7j4y2fEH/5AEFe5RlZ/276VRjK/j8a8vBIC9SpkRmQrFwJ\n48fD2rXFu/ySkGpJZdG+RXy18yv+OPIHXkYvhjYbylNtnqJZaLOyvjwhbgj79u0jPDy8SNseOgSv\nvw5r1qhB7UcegaFDr25Wblkzm80YjUZMJhMbNmzgkUceYceOHWV9WSUmr39vTdO26roeVUaXJPJQ\n6vGXUNVESSlqJTMXh0MlglyNrfObsuVadMVoAKORkymnmLX8LR5+dAb7KumMfKoOoyNH47VjKFX3\nHeKeaV1UFdALLwLw4UdQ9dI+7v72brV6bk6VK8NHH0PPXrlfO3AAnnwcDh+GJ5+CB0apgc28vPcu\nTHgZ/jqgqtoLcCL5JN/sm4fPB1Pos/48jwwLon2ff/NIi9HZm2jruhrMDQ5Un8PltOyfYV4czgRd\nhcDr+wYirilXEs8kJcHbb6tVYU0muPdeePppNYnkenWzxTPXo6uJwa651dPK1Jkz7scXEtUNPC9p\nGWDOAB9f9/zxvFisatnU+L3Qb6B6rl599f3wIZU0stnAmM/NNetxHA7YGqdGfpo6ExbR0fCxHXZs\nh9vaqDLm4rI74MxpqOq8iRsM0DzC3Qy7XD6/xVzLpDrv38nmZD6N+5T3NrzHmdQzRFVszvR2k7i3\nzl346yZscdvZnAyXkqCCa3UQ1IpIrga314py3uUY3mI4w1sM5+CFg0zeOJkZO2Ywc8dMutbtyrPt\nnuWOunfI1DUhSkm9ejBjRllfhWcdO3aMwYMH43A48Pb2Ztq0aWV9SUKIsuBw5K4mMhjAZlVT03wK\nqCQ3GMChcyTlOP/b8h6zds3i9y+smDQT1i8+Ib7dvRg0A9tN8OqSEAb1H4RxymQY+QDWKjVI+u5X\nHv17pIr1li6D2mGq/MFiVoOD9erlX9LZoAEsWVa099i9u0oa/fqLqloqQI3A6jwf9ST61k/RLsLP\nU5MZefINakW8y7Dwe3ku+kkaBjfI3hA732bhOT8vDWyOwltMCFFCgoLUINjrr5f1lXiOxDM3NvlN\nmdXZcyrda7OpldTySxpN+h+sXQ0/LS+4mbXFqkZsUlKgmTPRU72mKtc9fFjd5Kw2d/lvQccB2LIJ\nWkSoqW4ALVupm2XcZmjbTpXkFjZdLj92e/akEUBkJHz8oZpKVy6fFdIMBjBbuZSSyOS4j5i8aTIX\nMy7SNewOXmw9mdhbYtyjOP97A9PUT+gz6Vd+WtKAW45mYA8J5Lvv4Ndf1ZLa16r6FevzYa8PeaXz\nK3y+9XM+3Pwh3b7pRmztWF7r/Bodanco60sUQlyHGjRowPbt28v6MoQQZc1qy7vqxcukKmMK8NfF\nA7yxeRKz983HaDDycVI72iSshi8+p0PM4MztIlpAw4Yw7virvGn7iXOPvMyqpJb8d8c4tKZNYP53\nULOmp9+ZW+Mm6vi/LC80aQTAhj/RTp2C/72Nz48/MHfhepbrtzJQn8+Xe79hROOhjG87ltoBNVUP\nTbuuVvgF1fz7wN9qOl3HTrmP7VoFWZJGQniExDM3tiIsTXCT0HW1fH3duurnC4kqeZSTwwF//wV/\n7VfVRgVVGmVkqH5GAE2bq32tdqhVGw4dVCNH1iJ0nM+wQHqaOlZ0a/WczQ4BAWoO+ZYt7kAjJa3I\nbzkbux1On4aqWXr2tIxU17x7Z+7t98WD3Y7FYWXy3zOp93FDJqyeQGztWDaP3syvveYTG9rafV2H\nDsF0lXFunLyR2M5GUk5n8OqrOpUrq4RRlSq5T3OtqehXkbHtx3L48cN81PMj/k78m9gvY+nxTQ+2\nnNhS+AGEEEIIIXKy2nK3AAB3U+w8nE07y6O/P0mTr6L57u/vebzlIxwetYfRW3W1tOSgQbkO9fob\n0PbuWvzW6D9UXTWPe7c/D716of2yomQTRq4L6N5d9SQwmwvffuFC8POD4ffDDz/BAw/QY9FOLqxt\nxzONRjF7/3wazGjBYyuf4dTlk+5zXLgAPyyG/fvhzj5w/zC1ZFVWRqMabL2G23QIIcS1QpJGLnY7\nnD8P1WuoBn8XL+RdaWR3wPlz6vGxY6oUNr8bTmoG7NujppQ1aOAug61TF44cUsFBRgGVSi7pGbBn\nl7rG6Gj1nNWuzh0VrZpVu5ZivXi5eDfA9Az1vqpWVddksUKEqxn2tuzbzpsDvbqxecYEGv/QmSe3\nTyQypBnb/7WdxfcuJrpaK3UdrtEbXYcJL4GvH4RUhrgt1A7T6NPdxurf7UyceH0kjLLyMfnw79b/\n5tDjh3in6zvEnYyj9RetuW/hfZy4fKKsL08IIYQQ1wtXE+yiTHfXddLPn+aNTe9Qf0YLPt81k0da\njObo6L281+ktapxJU43f7h+RZw8kkxH694fuv/yfiiGfeQbD7DlqILI0dOuhKtjXry94O5sNFn8P\nPXqoa/P2hg+mwLvv4fPHat5a483BUbt4oMkwPts9g3qzIpm4dRIZtgy1DJXdDj/+BC++pH6ObgVv\nvekeENayLGgjhBCiQJI0cnElgypXUcuCXkhUN5xc29nhrLP30T9H1A0nv+0sVlUdFB4OXl6qvNjb\ny5k0cu5b0PQ2UNtkmFU/I02DyFbqOQ31Fd1a3Xz371MjUa6VNq7UiZMqYKlaTR3XoUNwsLrWrKWG\nO3fgGP8CAH/9PBNfoy/LOn/Fr7d/Q0TVCLVNcqra3xWsLF8K69bA08+oZQHiNruPZy7GtV5D/L38\neabdMxx+4jAvdniRRfsW0eijRry17i3MtiKMogkhhBDi5mZ3qOrzQpJGuq4T/9RQtIb1+XrxK9x+\nS0f2jtjCh7e/624O/fVXqopm2PCCzxkYCH+shPET8m+wXRI6dlTdfn9ZXvB2a9eqwdyBWaqlNA0e\nGgN9+sCC76jpF8pnXT9k/8ht9K7TnfEbXqPxV1Gc/HYaetWqqnXDc89D3Dbo2RPeeB2mf+E+ntFQ\ntMFbsyX/lhVCCHETkKSRi9WmEkWVK0NwRVXamtcNwmyBxET1+MgRQFNVP7m2czbB3rsHmjVXz2mo\nFcjq1FXzqE+eUN8Lqgyy2VUCJm6LmopWPkglpHy8VYAR6Wx2vmWzO9hITr3y93/8uPqetaeRrqsp\natu2gq6TeiaBi6Pv5bi/ld8bejEwIZAdfZbT45bb0cxWZ9Cjw4Uk93Kn6enw2ivq2ofdD1GtVcPx\nEwnqA0nPyH0taelwJlE1HM/rs3El0q6m8beHlfcpz8TbJxL/73juqHsH434fR7NPm7HsQBGbQwoh\nhBDi5pRXE+wcjiQd5d9TutHgyx/xtcG6/W1ZfNc8GlVs6N7IYoHZ30CPntnbDVxL/P2hQ6yq/inI\nwgWqwqhrt9yv3T0Yzp5VFVVAvQp1+e7Ob/ht0E8E6d6UX7OZpbca+TvpkNr+llvgy6/VysPTPnfH\nlq5G43ZH/teh6yoetRQhuSSEEDcoSRq5nD+vSlYrhUCFYJU0ciVBsjp1yv3ckcOAnnfvo/QMdxPs\nps3UPjoQ4O/um3T0sHvZz/xYrOr427eqMmJQKz6ULwe+3hBaVU2p2+pcGtfLBJeSr3yKWkKC+l61\nqrpOby/1/ltGQuJ5Vm6ay7bhHfG7mMI3z3TnthEv4X8hGdOhw+6VK8wWlcwxW9zz7z/+EE6ehFdf\nV03GWznfw5bNYDKoldeystrgxFk1ve3YKTh0HM5dVMdNSYNT5+HAMTh6Eo6fLl5VVQmqG1yXxfcu\nZtnQZWiaRq85vRi2aBiJaYllfWlCiDL0xhtv5PvahAkTmDRpUilejRDimpJfE2zAarfyv83v0XRm\nFCOmbcIaWA7Ho48S8vsG2PBn9o2XLYVz5/JvMu3II64tDl2/uuN0765WET5wIO/XLRb48Ufo3Uf1\nNMqpW3e1mtuC77I93aVWZ7bUmEiAFWbUvkDzr9vw9pb3sTmccfpDY+Dvv2H1KvWz5izbLyiWtNmd\nswdkGpsQIPHMzUqSRi4nT6nvlULU9LTE8+rnnAmdE1ka7R09oh7ndbNJS4f9e9XjZs4m2N5eqkKo\nTj31/CHnCEhB86kzzLA/HtLS3E2wQVUslfNXCaToaDXlS9dVssZmV/sVla6rZBhAlarqGOXLgc3O\npcb1AQh66jk6HDBz/PlHeWHYdAI6dlfbr1/rPAYqUXbxMmgG9fkcOQzTpkL/ge5rb9RIlURvjXOW\nBZvdn7Guw6lz6ruvt/rSNLhwSSWJEs5AcopKNvl6Axqcv1j091mKetTvwe5HdjM+djzz986n8SeN\nWRi/sKwvS4hr35ETsP+w576OlGyPMVtegwZ5KCjIEkLc5PJpgr3j7C6iZndg7LrxTDrakNuOOfD/\n3/sYxk+AatXgxRezJ2++/BJq1ICuXXOfw+5cYv5qp1m5+gBZbfkfy7WNxebe1m53X2v3Hup7ftVG\nf/wBly7CgIF5v+7rC33vgh9/UIvOZGFavhwCAvj4la30qtON59e+RLu5Xdhzfi8MGACVKsHnn2XZ\nwahi0fySYBlmNd3Pbi94kFeInJJSIPGS576SUkr0ciWeEQWRpJHLKWcyKCREJY4uXAD03CWrJ51/\ngNwarpIiRi13XyJdh3QzxO91NsFuqJI75XxVJVCFYJWYOnxIVegUlDRKN6sqI1CVRq6bmo83+PuC\nprunfCU4p5hpGly+gilqDh1On1LXGhSkrtHfj+WnVtPsr8dI9YLI02C/514aPPRftU+NGhBWB9at\nUz+bDHA5RZ3X29kA+7VXVOPCcS+4z2U0qr5McVmm07mSbucvqRLgrMufGg3qvbqSSN5e7rn33iZ1\nzrymuOX5Ph2qWimtiNtfJW+jN690foW4h+KoEViDQd8NYvB3gzmberZUzi/EdclsBl8fz30VYYWe\niRMn0qhRI9q3b8+QIUMyR8k6derEE088QUREBE2bNmXzZtWPbcKECQwfPpyYmBiGD8/eN+TUqVPE\nxsZm7rN27VrGjh1Leno6ERERDB06FIDXX3+dhg0b0r59e/766y8Pf4hCiOuGqwl2lr5Cdoedtza/\nS+s5HTmbfo6l7T7lkUXHIDYWhgxRU7xeeFFVbf/0o9rpn3/gj99VLyOjMfc57HYILKdir+ImP1zJ\nIH9fCAp099LMOvjnSib5+UKFAHVOP18wGN1VO7Vrw623wop8kkaLFkKFCtClS/7XcvdguHwZfs1y\nDIcDli6Frl2pWrEWC++cw7zeX3Lk8lEiv2nPazsmYx8+XG1zPEvM7HDkPQDscIDV6q6eL2gamxA5\n2Wzq7xZPfRUhqSPxjCgpkjRyOe1sbl3RmTSy2dTNKL9Ko9vaqN5GKcm5mzlbrCoRs2e3uil6eakb\nqZ+vCgpcK6gdOqgqdPIri83aBLvmLVCturph+XqrgMDV16hVlr5GAF5GSEouelBgt8OZ01BNzX9P\nxcyjfzxFzzUPEORfAVu7NtAyEuMrr2XfL6Y9bN7ovKEa3c0ENQ0O/K2Cl0ceU83Fs2oVDX/9BUmX\n1M8ZZkhNV1l0H6+irR7iOo/RAGcu5D9C5HCoY586q6a1HTulei6VohZVW7Bp9CZev/11fvjrB5p/\n2pxfD/1aqtcghMjbli1bWLhwITt37mTZsmXExcVlez0tLY0dO3bwySefMGrUqMzn4+Pj+e2335g7\nd2627efMmUP37t3ZsWMHO3fuJCIigrfeegs/Pz927NjB7Nmz2bp1K/PmzWPHjh0sXbqULVu2lMp7\nFUJ4iCeXaXc1wXY6fOkIHb/twbh1L9Ovfh/23L+Znp//oSrO35/sjpHuG6oWWnn5ZRWHzfpaPT/8\n/tznsNlVEt3bSyV8bPYrfw+uhJCfMyFvMqqEUIC/inktVtXj08cbKgSq7YxGFfP6+agK9gB/sGep\nNlq3DpKTs58nIwOW/Ax39lUDj65z5xQbq5be/e5b93Nbt6pB1F59ANA0jXsaDSJ+RBwDGvTlpT8n\nMqjKSvVxz5zu3s9oVIO0Oc9jsYKuOdswaNIMW1zTJJ4RJUmSRi6nT6vvISEQUkk9vpCYe1Th9Cl1\n43BNt/rnH+dNJcuNxmxRyYqsTbBB3UhBJX3q1FPT00xGVS2TF7tD3aDjtmTvZ1TOXz02GVUAUL8B\nBJZ3J40MBnUDTy/iFDVX0ii0KnHnd9BycTembv2M/2v6MHHdfyRo+nz4dhH4+GbfL6a96tm0a6f6\nTAyau8po/lyVLBt8b+7zRTvfy7atap/kNDh5Vr2foiaMXEwmVWmUnJb7tbQMOJSgeh8lp6lr8/Eu\nk2aGXkYv/tvhv8Q9FEeIfwjdv+nOcyuew2KXxopClKX169dz11134evrS2BgIHfeeWe214cMGQJA\nbGwsly9f5tIllezu27cvfnn02oiOjmbmzJlMmDCB3bt3ExgYmGubtWvX0r9/f/z9/Slfvjx9+/Yt\ngXcmhCgRuq7iNk8lELI0wd7x+N0ENWrG2A+2sDnlPubX/y+V1m9XvXueeRYaNHDvZzLBKxPVAOQX\n0+CbWdDlDqhVK/vx7c4qJn9nDOeq3s7r+l0VNxarij9zVhD5+agBUFespmnuJFE5P1VZVM4v/9XY\nDJqqkAfV18hqhVUrs2+z4leVSMq6apqrv2dWRqOavrZ8OSQ5BwOX/Kye75a9eXZl/8rM6/0V83t/\nxUrtKEsaGciY/pm7EtVoUJ9T1tWQXbMGTM73YjCo6xXiGiXxjChJkjRyOXMafHwgIBBCKqvnLlzI\nXa1z+jRUrKSmnAH8c9RZ9ptlu9QMSDimbnquJtiaphI8oEZowuqovkkpl1WlUl5T1CxWOH1Sbdcy\n0vmk7r7xg3uEJyYGfv/NfVM1aKohdlHYHeinT/O3fzoxvw0mw2Fm5YiVTOryNr44q5pMptz7tW2n\n3perr5GPt7qpms2waAHc0U0l4bLSdWgeoY4Xt0UlipJT1XswGXOfozCapkaxzl7IHtxcTFJVRRru\naW2uxJbVdlWjhLoOM2dCmzZQrx48+CAcPly0fZuFNmPzQ5t5uNXDvPPnO8TMiOFAYj6NIIUQZU7L\nkch2/VyuXLk8t4+NjWXNmjXUqFGDkSNH8vXXX5f4NQohSpFrQK+oU+MLY7WRaktj5PJ/4ffTMmx+\nPvRIDiV60hy01tEwsL9KFj31dO59u3eHDh3gxRfUoiMPPJD9dde0tAC/7INyrsRP1hjXZlfvLcBf\nTT3z83VXw1vySBhlpWkqts05LS6nrMmk29qolghvvA6ffgJ/7VfXu3CBih1jY93vwWhQ1+JwkJoG\nn3wCg+6GcdsHg9mM5fuf1bZLfob27SE4OM/TD240kB3D/mRFt/r4Xkzm81f7kmJxDtwatOz9QG32\n7NMGDVrxKrSEuEZIPCOuhiSNXM6cVckiTYPQUPVcYo5KI11XZa9VqqiRHFezZ43sIyBp6bAvXj1u\n1lwdw8fbfaP19oa6zmbYR5zZhrz67Jgtqi8SQLNm2fsZubgSSHf1h3NnYb2zx5CXSfXvsRc+EnY5\n5QK20ydYbNlF16rt2X7/BjqGdcyenMpLhWCVFHP1NXJZ8StcvAj33pf9eV1XU9iMXtCkKWzZ4p6u\n551HUqqoTEb1+V9yTsk7fR5OJ6pj5kxEuf4NrmKE8OWXYcoUeOUVWLJEreTavr17AbrC+Hv582mf\nT1k0eBGHLhwi8vNIvtv7XeE7CiE8LiYmhp9++omMjAxSUlL4+eefs70+f/58ANatW0dQUBBBQUEF\nHu+ff/4hNDSUhx56iNGjR7Nt2zYAvLy8sDpHqWNjY1m8eDHp6ekkJyfz008/lcA7E0KUCJtzpTNL\nPgN+V2jfmb20nn87v2yaTaNEqPzUi5j2/gU7d8OUD9U0tGnT1cBmTpoGr76mKmCqVIEePXNcq10l\ne3IO/BkMKpHkSoK4GnEHBagY02RU+1UIVF9B5fJPGF0Jg0EtlqLrqhr9zbdUzPz8cxAdBeGNVGB1\nVz/3NdsdattyftjNdv7zmM6JEzDxVRj2QRSJ5etw4M1v0Q8eVK0PevUu8BLCgmrz7st/cr5GRZp9\nv56o2R2IT9zn7s/kivvN5uxJLk1D9TqVKWri2iTxjChJV/GX+g1E1+H8OajsTBpVV719uHghezLI\n7lCJmdBQ0A1Qo6ZK+uioG66vj7oBW22wY5ta3aFhI3WDCQpwH8fbBHXrqseHD0PT5qraJus2oMpi\n98Wrm9atjd0rsGVNhPg6+xp1ul2N2Hy/EDp2Uu9Dd/bzKZ/juFnsPL2TMV/cxSabg8gmXXmmw1QM\nAc5KKy9n0sXucDcBzCmmPUyfBqmp4MpUz5ujPpv2HbJva7E5p4dZVfPub75SN+W8AqEr5W2CcxdV\nI+4Ms3vltfxYbdkbbhfRxYsqYbR/P1R1/mcyYYKqjP7wQ/jf/4p+rP7h/YmqHsU9C+5h8ILBPHPi\nGd68401MBvnfUojSEh0dTd++fWnevDmhoaE0a9YsWyDl6+tLy5YtsVqtzJgxo9DjrVq1infeeQcv\nLy8CAgIyR+bGjBlD8+bNiYyMZPbs2dxzzz20aNGCKlWqEO2asgtMnToVgIcfftjD71QI4REWZx9H\ndEhPB1NAsZMps3d9w5if/kU5L39WVHsOeBtDjDN2qlNHfY18oMBj0KoVvDxB9b708nI/b7er+NEv\nnwFALy8VK6Wb1Tb++SSFjMbCK4iuhJezIbbRqJp2DxsOR4+qaWor/4Cdu+ABd78VVYmu2gus3myn\nnI+F114zOS9VwzHmboInTeL0mzOpBtBb9TNCd/ZZcg1OZmEyeRPy+FhCnn+OWofO03pOJ2Z2/5S7\n69yp9vHxUrMA8ooTbfa8q++FKGMSz4iSpOnXcJllVFSUnrOJV4mw2aFJE6gdBh9+qkZVqlaGJ56G\nseOgqnOKldmiyko6d4aXJsLDD0LyZZj/PVSpCBWDVJLm+GkY3E8lUeZ+p6praoaqkl9QyZ/4QxDZ\nBEaPgWfHqoRKg1rZRzUOH4fRD6hV0X79Q52/QnkIrZT9+g85V4AY/1+VNNqyQ53bYoXAAKiWY4qY\n09zdcxn14yg6nCvHr5MT4dPPodMdUP8WLqeZWLAAKtnO07pRMlVreecdE61bC8OHwMyvVeLq+DGI\nbQdP/R88/pR7O1eTxNrV4J9TsPI3eHQMLPxBraaWuZ0DfvheVWjVb5D7fKASeVvjVEIuawmyxaoS\naN6mggO4DAtUr1xgMi0/69bBs8/Chg3Zn1+xAt58U60Se6UsdgtPLX+KT+I+oXNYZ+YNmkeVclUK\n31GIG8C+ffsIDw93P3HkRJFWPCsyHx+oU6PATVJSUggICCAtLY3Y2Fg+//xzIiMj6dSpE5MmTSIq\nKspz13OTy/XvDWiatlXXdfmQryGlFn9dbxwOuJisEh+uaqPyAVc8CGVz2Hj6l6f5cPOHdKjelnl9\nvqb6hEkw+xs4lsDJc178sVLlPTp3hpoF/wrLW1GuzeFwVvKUYhIk3aym9hX1nBabGlQ1GXllgk71\nwBQeelB3J7L274PW0TgMRgxNGsN6Z4Bms7sHWS3OBFDW2DApCW5tSFqfHtxxewIbTm3imVaP82ab\n8ZjKBbivcccOeO5Z+G6BamFhMKim3kLkkOv+lpRSpBXPisxkyl1gkIPEM6IgVxODSaoc1GjM+fNq\nVZHQwuYAACAASURBVC8dlWgJCFSVRtYsZagWq+ovVLmKWjq0dhj8tFhNT3OtHJZhVlU38Xvh4X+7\n9/XOMvpjMKiqpNq1VQNDTXM33CvnbETmcKgbZfweaBujntNxv55VgB9cSoH+A2HON7B8mWogaDBk\nn5/tersOOy/+8SJvrX+LDrU68G2lu4HHIbQqaLB1h5HefVSbpJgIf2znk7FthEGD8hhsiooCbx+V\nTel0O8yfp8476J7s21msEFJBjWZ5e0Gks0fTls3Zk0aT34MpH6jHka1UI+3ed6ok2L54tQzrj4tV\nxVdMe5g1N8u0Py+KRCP/FesKUasWHDyoBhez9ozbtQvCwop1SLyN3nzc+2Na12jNw0septXnrVg4\neCGta7Qu3gGFuJ4VkuApCWPGjCE+Pp6MjAxGjBhBpOv3kxBCZGV3Nq12xR1GoxosDMqj2sjhcK+6\nlUViWiL3LLiH34/8zpNR/+Gd1i9j8vWFP9dD69tY8KMXn3wMd9yhZnKNGAGjHwRnD9uicfXSLKxX\npMGQf9PqknIl/St1XX3ezmr3W2pprFjuz0MPJDunumlwazgJwc2oeXG3u8rIta9rqXKzRf07GQ3u\nQDYoCAYPxn/ePFa9d4CnNr/CpK1T2Hp6O/N7zqRygHPw7uuvYOMG2LhRNdi22dyfrxAFKSTBUxIk\nnhElRZJGoFbTunhBNd4zGNQNrWJF1Qg769zl06dVEFA5VK2mEFZHNbu+dNE9xSolHfbtVvu1aqUq\nbPIojcXHB8Lqujsoa6geRK6kkMUK586pHkpN8+ln5OLvp0a+WkVBrdqweJFKGrnmZ2e5uV02X+a+\nhfex5MAS/tXqX0zpOQXvNyap41Spim40cf8IjQ8+gHvvBew+2P+Cb77T2bZNUwufuea/o4Gvn0oc\nrV+rbqQL5qvpcdWru6/PZlfvv6KzRDLAH6wV1ee3NctI5u+/qYRRvwHQuAl8Ow/GPguvvgzVqqsE\nm5cXdL5d9Z+a843a546uV/bvbTC4k3xFlZIGJhO1annTsSM8/DB88AFUqKCqi95+G5YuvbJD5jQi\nYgTNQ5sz4NsBxHwRS+iGL7Fuv5fOndUUuFtvvbrjCyHyNmfOnDyfX7VqVeleiBDi2ma1Zq50Brjj\nLIvVHZ+5+jemp6sBQn/3CNPes3vpO68vCZcTmHnndEaGDVRJjAsXYO9ekh/vzycfw9ez3NVFDzwA\nw4ZBuxionWNhtHzZ7Nl7aV5LDM7eQEWh6yredr6PwYNh/HgjXy7wY+hdqhLo22/BHHwPoy7uhj5Z\nV4vS3avy+jr7OqWkZW9P0H8AzJyJ95p1fNz7faKrtuLh354g/IvbCf9zIeXTb2XurmWUBxWvdu+u\nLt3uKN7iLUKUMIlnREmRRtigEjO6rpJGJqMKAipWgguJ2csKT5xQ3yuHqOGf2mHq53+OqsSTrqvK\nnu2qURiRrVTyyM8n943bzxvq1FX72pw3sMup7uSQxQr79qjHTZqq5JOrx1BOvs5ARdOgX3/4c51a\nDc5VweR8DwcvHKTNF2345dAvfNLrE6b2mYq3wQtOnVJBS0glzl4ykZoK97gKhYxGjP4+dGjrID4e\ndzDk5eVedSOmgyoPXvid+izvyTIcpuuqWiu0kns0y9VgOyoatm5R2xw9Ak89rhJkb/4PHvqXmpK3\nYLEKAkJD4dXXYdM2+Gw6TJgI9erD66+qz/5KGAxF30fXIfGSmnJ48iw4HHz5pfq4atdWfScffRSm\nT1c5wlwup1xRVVPLai3pcWwLfhejOdF2CMO/eJXISJ1OneDYsSIfRgghhBCeZraqSvOsTEY1lck1\noJaUopo7G02qgtzZLPunv36izfQ2pFnTWHX/SkY2GKwSUAYNNm0EXWeTKYbbu2SfjlY1FLp3u8Lp\n7zqqL8+1yGAAtKKtQmZ3ZOsfFBCg2gF8OcebQXdDt64669ZB14WPwrLl0Ly52lDXVZyetYrKZFTT\nynTc545pr0b/nA2DhzYcRsc9v2DWM9gZ24WH75tO+SS1yonubAIMeHbKkRBCXAckaQRw8pT6XilE\nJWYMBqhUyVlp5HDfXE6eVN8rV1E347A66ud/jqqkTpozaHD12wmqoPbPaxUyH+cKalar6gNkMKgE\nk9mZYHA1wQZVdWO3qyqkvEaNTM5kksOhqnQcDv6fvfMMj6rc2vC995T0ACGh96IgSBFURCkiICAC\nIl0QVCzYRY/6Hdvx2LGgyBF7R6pIU+moFLFTFOmKtEAIJaRnZu/vx9o7M5PMJJMQJYH3vi6Yye5T\n3zXrfdazmDdX1mlArodv93xLh7c7cCjjEEtHLWXc+eNkvWFA8gHLBFzHo7kKnyIuGqfmxe0yJGFU\ntZJ4E9nnvPgS2e6pJ0QB1K27b99cD8RFB5bV2eb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wSLxSkjboHq9vxnfRF1CzJjz8CAwa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UJRPIYhCaGwtvVLGiUfkPuqPK1ikp6bzoDpAzBNk3nD5hEXEXeqL0mhKDkOhxhl164mf3uLqV1P\nTIT3P5IvvutGwRtToE9P6N0D3ntHgpQ3pvi21zQxHrWy6kMb9uPVyMF89OtUXt/6kW8btxMOpMCf\n+6WjmgpQFAqFQrFgPjRpKt2ipryWv3hDyiaWvvsQAIPGTUYraubWawSMQwpFhcXtCh4fmaYki5wO\nqWBr1Qp+/10+NxaapvG/bi9xUc0LGb3oZjam/Cor7rkbRgyHqR8XPq6myY/X4mJDhUJRPJ4QpWkn\nTsC4W2DnTvlbMwsojQ7J77XExH/uWsNEJY2KwTRNxswdw28pvzFz8EwaJzQ+1ZekUJwcbhfUqFp8\nmRpAw0bwzvvS/vHZp8SU8T9PwLqfYNAQmD0TDh8Ovu+mjdz+4CxmranFHd89wqqD38lyhwOiIsQg\nbs8B2JsM2TnBj6FQKBSK059tW2HLFrj5ZujfH956C9LSOJx1mP7zhtJ7p46nQT0imjYLfQzTJF+B\noVBUdBx68BjNa4gKSdMknmrVWuKpzZsDNotwRvDplVOpHFGJAfOHcXTnr7B1K1SqBLffJv5hhTDl\nWAqF4uTIC2GC/crLkrS1P38mYFqJWsMQpVG1asV3PDwFqKRRMTy16ik+/f1Tnu/xPN0bdT/Vl6NQ\nlA3xsaI6Cqd+vW07WPAlLPsa5i6E0ddJx7WxN8vM1scfBN/vuWcA6LPmEJ1zajDoq5vZk7Hft97l\nFN+JrBzYvV8ZZCsU5Y30TKUEVPwzLLBKZvpeCePvg+PH8b71BkMWXkvq8WS67dZxdr+86GMYhpRf\nh+vholCUZ3Q/XyN/TL/EqNMhSiMoVKIGUDO2BnP6fcK+9P28OXmMLJw1G9q0hdHXSrmaPw6H8jVS\nKMoCr7fwWJScDJNflfvbt/mW2+VphrVNjfJXmgYqaVQkC7Yu4NGVjzKy1Uju6XDPqb4chaLs0DRR\nG2m6fLEVR9OzoHEBlV3jxtC9J3z4PmRlBa5bvQrWrIKbx6E5ncxZ34wsbzZXrRxLlsdvW02T4Mfp\ngL2HIDP7pB+aQqEoI1KPqRbMin+G+fOg/flQuza0aQPdLiPjlQl8u+sbZlf7f/bOO7yp+vvjr5vV\nDQU6mSqCqCiiDFGGA2XIRkCGICKouLf+HODAvdfXLQ6WIFsUEGUoSxQVxcGmlC5G6R7Jvb8/Ti5J\n2qRNS5GWfl7PkyfJ3Wlvcs99f855n1ux5uVD93IG7nRDStMUipMBTROz65K/wQaeLASrFZo0k+wh\nP6IRQMfE9rxz+Ws02vg32XXDoENHmDMHTjlFjOe9TLSxaOIzpn73FYrKo+uSPVSyPO2ZKdL84dTT\n4F+3aGSWhcqKkJZWLf2MQIlGAfn7wN+MmjeKtoltea/Pe2XX0CsUNRGbDRJjxBS7stkE42+Ew4fh\ny9meaboOzz8DjRrDXffCdddT9+sVLEi8n58P/s6EdQ9glNyf1Qo2CySlSuaRQqE4sRjK20LxH7F3\nL2zeDP36HZ30zeA21MnM59OD3eixzd0pqktZHdPc1xR3pzWF4qTANMM20Q0Rdkyjd6vF42v02+8B\nNzP27FH0SwpjUZN8Pvt7lphrz18oYtOgAbBnjyyoabI99duvUJSPrkN+Qel7KH8m2P/8DZ98AuNu\ngG5dfUUjc/BedxthJ8Qf90OvDEo08sORgiMMmDmAEGsI84bNI8wedqIPSaE4PkSGQ70oyC+CwmL5\n4aqIgNS+g6Q5f/Cu50dvyVew5XcRjEJC4MabITKKS6f/wBPn3cvnO+fy2l8flt6WzQpWTYSjgiLP\ndMOQ2mB/P8wKheL4oOvq+6b4bzC7OfUV0ein1J8ZcPBNtp4WxdVLdsGypXDhhRDlpwmJYci1p6hY\nGWArTj5sNt9zWnf5enZZLIAmHdT+2BLYj2jrn9TJzCepXQvGL7+VTam/SFbf/AVw5IiP8Twakg2h\nUCjKpqhYyvhLlnQ6deSL5MXkyRARAfffL9UbBw7AwYPuTCO3SFtQKNNUeVrNQDd0Rs0bxY7DO5gz\ndA5N6zY90YekUBw/NA3iGkDjOIiOlACksFhEG2cQZWuaJtlGe/bA8qUSaLz0HJzRCgYMlGWi68GE\nm+DbZTzsvJiBTXty76Yn+S7lx9Lbs9nkdzYpBQ4dgX1psH0v7EiSbmuHs6r04ysUigAo0UjxX7Fo\nIbRuDc2bk5abxsCFw0mITKDxpJfR9u4Vg9/LvUrTzIGEomK5TlmsMgASGnLiPoNCcTwwM4rM32Ld\nkOwjEzMzqE0bKCgQQ3l/fL8SgBtum0p8eBwDFw4nPS9dbl579oQ5sz2Ck8UqcaBCoSiboiK5b8nN\n9y3pdLl8TbDXrYWvFsOdd0FMrHzvALZvk+XMddNS5VmVp9UMJq+czOJ/F/Nqj1fp2qyMVGiF4mTB\nYhFj7PgYOLUxtGwGjeIkgAjmprFHL2jaDN57B2bNgN274f6HfJ3/x46DBjFYXnyeTy5+hTPqNGfo\nqpvYnZNUent2G6BB+iHJLrJaZAQ5xC7TVKc1heL44zK86uwViuNEWhqsWwd9+1HkKuLqxaM4VHCY\n+f1mUqf/MDjzTFnOWzRy6WC3Qt1IqFcH6kSIYKQMsBUnG5omWdhHf4vd773nW61wjmmGHaBE7fvv\noEULGrRow7x+MziQf5Ahi66l2FUM1wyH9HT47jtZ1ryJLVZd1BSKgLh0KNY938fcfM89k3fnNMOA\nRx6BhASYeItMa+kWjbZtk2dzkG6/u1lQfMJ/8xkqiLrCejHvr3k8ufpJxp43lontJ57ow1EoTgwW\ni3RWqx8d3GiT1QrjxsPmX+DZKdC+I1x6me8yERFwy22wfh1RGzYz/7IPcOouBn5/A3nO/NLbtFtF\nKLLbPDcCFosISMnpqt5eoTjeqEwjxX/B11/Jeda/P3etfIAfktfx4ZVvcV7cufKb/+zzMGSop0MU\nyPKhIaVLdxSKkxG7XX6PdV1ioJLiqM0KzU+XOGvVytLrFxXBjz/AJZcCcH78eXxw5VusTv6Ru1c9\nCFf2gHr1YeYMzzpWK2TnQGFR6e0pFAqprDAvP3abZL4WFcv1SfcywV60EH7aCA8/It9RgGbNwOEQ\nXyNzOd2QzmmgMo2qO1sztjJ6/mg6NOrA21e9rYyvFYqYaAnMiwKMNjldHvHm6qEQHQ25ufDg//kP\n5EeMgoaN4PlnaKHFMr3rG/x2aCs3rL23tDF2IOw2UfDTD6obWoXieKJEI8V/waJF0Lw5Hzp/4u3f\n3ue+dncyvNVQz/xLL4UPP/LcKCvDa0Vtw2b13Ig6/Jz3VovEXKOuhVkzYft23/kbN0BeHlzmGcwb\neeYw7jr/Vt789V0+/ncWDBok5TPZ2Z5tWq3i15JfqK4FCkVJiop8BVybVbKNnC7A8NwHvfEGtGgB\nI0d5lrVapQO1aYYN8v1OS5PXiSdxppGmaT01TftH07TtmqY96Ge+pmna6+75v2uadn5V7LeqyCzI\nZMDMAUTYI5g7dC6httATfUgKxYnHYoGGsaW7KBmGeB7phid9OTwcHp0Mt94B51/gf3shIfDQI/Dn\nH9Dzcnpv13iq7f3M2LWAl/58N/jjCrFDZjZk51b6oykUinJwKdGoplBjY7DDh2HNapIva8/E7+/m\nimaX8Uznx8tex+WCEGV4rahFHPU1wtfP6Oh8q3wf7rsPQkNhylO+87//Xpbp3MVn8vNdn+KyJt24\nacUdbL2iLeTnw8IFngUsFtlfXj7kqUYkCsVRzNI0q5eMYgpIeQWezmlZWbDpJ+g/oPRAR8uWHtHI\ncJeEpqbIdzUm9rh/hMpwzKKRpmlW4C2gF3AWMFzTtLNKLNYLaOF+TAD+d6z7rSpcuouRc0eyK3MX\nc4bOoVGdRif6kBSK6oPDDgkxnpRLp0tK1qKj4LRG8iNpGrgNuhruua/s7fXpC3PmQ3gEjB3NQ1O3\nM6ZBdx745WmW718d3DFpmhxXyoHSHQsUCkXVUNFOiooTQo2OwRYtAqeTCaHLaRTZkJm9p2K1WMte\nRzd8u0cpFCc7FnfWj2H4ekV6zzeAuHi4eSJ8OQd+9/I2+v57uKAd1K3rs5rNYmNWn09IjEjgyqSn\ncJ7azLdEDSTestvESzInT10TFAoI3F3QbhM/WHNQ48cfJJa65JLSy7ZoCbt2SsaShls0SoX4+Grr\nz1cVR9UB2G4Yxk7DMIqAmUD/Esv0Bz41hPVAtKZp1aJgb9LKSSzZtoTXe75O56adT/ThKBTVjzoR\nUDcK8twG1E0SREiy2aBeVMXNEs+/ABZ/A7fcjrZwPh9N3swtexK4ZvVEdmXvDW4bZjr23hQ4kqMC\nGYWiinEWF+IyguigqDjR1NgYTP9yDmn1HKyMy2N+v5nUD6tf9gqGIcG0rRxhSaE42XDYRDDydzNp\ncXdQMwy4/Q7pWPv4ZJmXmQm//Cxlnn6ICYthfr+ZHCrM5JPWLozVq2HfPt+FzIG6Yifk5Kp4S6Eo\nKvLNMvLGbvNkBH7/vWT/dehYermWZ4igtHsX4K7oSEuDBLk0FzqrX9OfqhCNGgHeLZD2uadVdJn/\nnLl/zWXKmimMazuOm9rddKIPR6GonmgaxNcXoejURhAR5plXJ1JGuCoaRISEwL33w8IlWOITeP2j\n/bw4L4/hS6/3b4ztD4dNAqWUDNiVrEbBFIoq5IEfJ9F7zTiKXMoItZpTY2OwVy6ycEv3Ij7u8Q7n\nxrYufwWnS8qTVWmaorbhsEtzEH9omjvbyBBvybvvhuXLYO2PsGa1ZDB4i0bFxT6x0nlx5/LhlW/x\n9Kn70AwDvpjlfz92GxS5xBpAV81IFLUUf6Vp3nhfn1athE4XiXBUkhYt5Nk0w3a5y9MSEihwFtB1\ndk+mbHihyg//WKh2+U+apk3QNG2TpmmbMjIyjuu+EiMTGdBqAG/1fksZXysUZWG1QoO6pVOjzUDG\nGSAjwTRvDMRZZ8O8RTDhJsZuLOLD5//m8ZnjgzfGtrq7rOkuSEqVzCNVe69QHBPTt0zn5S3v0DLq\nVBzWADcqipOO/zL+Agi77EpaXXcvQ88YFNwKhiEdZxSK2obNJo1Jypqvu+OeCTdKe+/Jk+G77yAy\nEtp3kHmGIQN9JTLEh7caysArbufHJnD4k3cCx1AOGzh1JRwpai+BStNKkpYGf/3lvzQNSotGSPc0\nIyGBm1fcyca0nzknpmSl+YmlKkSjZKCJ1/vG7mkVXQYAwzDeMwyjnWEY7WJjj68RVKcmnZg3bB4h\ntjJ+iBUKRWA0DerVlRRLfxQWy6Os4MLhEIPsT6fTzBnB45NXsvrJ6+C7FbB4EXwxEz7+ENavC7wN\nm03Eo6Ii2LPfLR7lK/FIoaggm1M2M27hOLrGX8jLbf7vRB+OonyqLAb7L+MvgIntJ/JUp0eDW1jX\nZZAg0OiuQlGbsVnAcMdZ4eHwwIMSM02fBhd3BrvbB0zXZbDPbis12PdslyfYdElL6u1K4Y8VJbyN\nvLFbJStCCUeK2khZpWnerFolz90u8T+/Th1ITPSIRvkFcOgQG9jH1D8/Z1LHB+nX/KoqO+yqoCqu\nvj8BLTRNO1XTNAdwDbCwxDILgdHuDh4XAkcMw0ipgn0rFIoTTWQ4aBbPKJdJsVMCk9h6UOgsX8Dp\n0pWIZT/yZ+s4un28AsaNgdtuhgfuhScmwchhsHpV4PU1TQIjUzzam+LJPFIoFOVyIO8AA2cNpK4t\nhjssb/PbZjsrVijttZpzcsVgLl2uHSVPOqcuv+0qK1yhKI3VitTruxk9Bk49TTqieZem6YbEZRFh\n7kxwz/fMZrFx7cOzKbTCulfuIjU3LfD+7Db5rmYp4UhRiyivNM2bld9LuWibNoGXadkStm2T61qq\nXJI/OrCMi+teRfjaB3n7f5KsVF04ZtHIMAwncCuwFPgL+MIwjD81TbtJ0zTTKGgJsBPYDrwPTDzW\n/SoUimqC1QJ1I33TnXW3qVvDOGgQDZFhUFS+YbYWE8MZX6xm+N3NuGJiJElzP4M162HtRjGNu/Vm\n2LGjnI24xaMQh3RX25sCWTnH+CEVipMbp+5k2JxhJB9JxTltHo0j6hMWrvHAA7wAqcMAACAASURB\nVDBunBKOqisnXQzmcslvd7FTriHe+Gs3rlAoxAwbrx9pux2eeEIyuXv09F3WapVHRJh0evL6ca/f\nsDn5l3ej/y+5XD9rWNmednabrJuVEzjbXKE4mQi2NM0wxM+oa1f/HQ9NTm8B2/4FIHWndDzMDEsk\ncdV7NG1kwTCgWzf4/PNjPO4qQgvaO+QE0K5dO2PTpk3HZdtbtsC770JyMnTqBOPHQ716x2VXCsXJ\nT36hlIWFuFOgC4sgtr4IRiCBya5kEXSC6HyzI2s37b+6isYRiazrtZAIezjsS4L+V0HdaJi3UJ6D\nwRy5bhwvWVEKhaIUdy+9m1fWv0L40qn8PXM0TfJ2A5DXqCkXdLDyxhvQvfvx2bemaT8bhtHu+Gxd\nURmOZ/xlGPDVVzBjBpwRn0WHiyxccYWGFV3ue+tGyk1oTh64DLBqclNcJ+q4HI9CUeMxDDicJfGV\ndzZefj6EeTUvKXJCdJQnUyI3DwqKxavI5OefcV1xGctOcbH42et568rXy963WeZWJ6LsG2SFoqaT\nlQ065Wca7dgBbdvASy/D+AmBl/vf2/DA/eT/9SePvdybF97fw129pvP8tH7YLTpoGn8mRdKlC+zd\nK/Zkx4NgY7BaWRy+cKEEvwkJMHIk/P47dOwI6ekn+sgUihpKqEPq5F06FLukU0D9up75NptkHfkr\nO/BD8zqnMKPrW/yZ+S/Xr71HjLEbN4H/vS/i0a0TRYgKBqtFavCT01SpmkLhh89//5xX1r9C96jb\n6Nt0DE0auTM8NLHHuO46WLz4hB6i4iTinnvggQdkBLVjB5g5E/7v/8BwuiAsxD24YJPunKF2uaaE\nKO9JhSIg3h3UvPEWjAxDKtgsXqJSWKiIst5ZfRdcgPWFl+i1HeJf/4gPtkwte982q2z3SE7gpigK\nRU1Hd9/fBFuaBoFNsE1angHAK7NuJ3/fHgB6XNXRJ6n27LOhbVtYvboSx1zF1DrRyOWC22+HOXPg\nkUfg6qsl7at7d3jppRN9dApFDUXToF4dKQczDEiMKe09EREmmUeFwaV39mh0Cc+c/yBf7F7E83+8\nLRM7dIQnn4YfVsPTTwZ/fGY6dlKqZEUpFAoAft7/M+MXjadbs25c1/AlsrMp5U+Wne1776FQVJa/\n/oLp02HtWpgwAXr0gPfegb27dX751SKDDyYWC0SES2aE93SFQlEam7XsQTndKJ2JZLFIBrbL5bvu\n9ePQR4zksdWw5O07Wb9/Y9n7tlplW1k5yuNIcXJSEUF01Upo2FDKz8qiZUsA9mxawdC6F6FrVg5b\nSzehqC4xWK0TjbZvl9/LLl18p48ZA8uWnZhjUihOCqIiJCCJry+eFP6IiZa2sQVFQWUc3Xf2zQw7\npR8P/fIs3yS7lfthw+H6G6Sj2uRH4UhmcMdns8qIWlKq7L8s8gsg45AyclGc1KTnpjNw1kDiIuKY\nPWQ2/fvY2bABNqzT4auFMPVD9uyBDz6A4cNP9NEqTgZWrID+/aGuVyKqwwF9euosXRXi3+jablMG\n2ApFedispRuSeGPo/u0BbDZ3prjXTbGmYXnlVZzntmbqlzr3fDSUlJzUsvdvZmDkq4xuxUlIUbEI\no+Wh65IWdMml5V63vnNtI88OvZ2n0sV6Ks6YBGbMsnDoEPJdtmgsWACpqaV1ixNBrRON6taFI0eg\noMRvWkqK8jRSKI4JmxWaNoS6ZfhOWCzQJB6iwkW4KWdEStM0PrzoRc6p14rhq29le9YumfHQIzBq\nNHw6FS7pDFM/Cs6gzmaTNOqklMDCUUEh7E2FA5nSGUShOAkpdhUzZPYQMvIymDdsHrERsURGSqnQ\nbbfopH3yFTmfzubii+HRR+Hcc0/0EStOBqKjJd7ywYCDh8AWobKJFIpKY/VTnuaNgcRA/ggPFa8W\n7/XDwrBNm0V4aCTvfXKQkXOuodBZTqa2zSqxVbD2AQpFTcAwxF4jmNK0LVvg0CHodkmZi+0+soeh\nS65jT1wIvYtPRUtJxdEkgb79YPBgePppnaEjbdx0k1RHBfrq/pfUOtEoIQEuvhgee8wjqmdkwOTJ\n0iFGoVAcA8G0RLZaxd8ovoGYMpYTXETYw5l/6YdYNI3+340juzhHfj2ffBoWL4WzW8Pjj0GvK+C7\nIPqDm8XCSSkiEHlTWCSZSBZNRt5SD8jogkJxknH30rtZvWc1H/T9gPMTzz86vXt3WLlCp67rEJaY\nBmzeDLfccgIPVHFSMWAArF8PS5Z4pv291cmnXzgYPqLWhaQKRdVhscigWCAMAmdKWK3iH1ayBKdZ\nM2wff8ZZ6fDKlE28+8JQjLIG+zRNbqxz81WmtuLkwaVL5k/J+5u/tkJamu+0IPyM8orzGLDwGpyG\ni0YXXIJ9x05IS4XERMbfADNnQbt2MHqslV27oEOHqv04laVWXqE//FCClubN4corpaSwd28YMeJE\nH5lCUUvQNDHKbpYIaCLWlBFgnBrVlC+6vcM/WTsYveYOdMMdtJx1Fnw2A97/WLKWxo2BoYNg/dqy\n928KR3tTPcJRsROS0jzzrRY5zv0ZqkZfcWxkHK5WAfTHmz/mzZ/e5J5O9zDy3JGl5oeH6oTmHSK8\nUX1iS5fXKxSVJjIS5s2DG2+UoPi222HyJJj0dAhNmpzoo1MoajAWC2hlZBtplJ0pERoCGKXXv/xy\ntM+n0USry+3PrCClaxtY+2Pg7Vit4NTVgJvi5MHpBK3E9yI9Dbp1hfPOhWefgVx3ZcLKlSIsJCb6\n3ZRhGIxbNpHfM/5geq+PqHP2BbBnj7RHS0gAID4OruwOffpZCA09jp+rgtRK0SguTsoNFyyAu+6C\nv/+Gp59WJfMKxX9OWCic0lC65BQ53WnNLr9Bz+WJnXmx3aPMT1rKU7+/5pmhadD9Cli6AqY8K93V\nhg+FUcNh88+B9213l6rtTZXWzkmpIg55ty2wW6U+/+CRqvvMitqFYYg5aDXpKrN+33pu+uomup96\nOc92f9b/Qi4dDh+CevX/24NT1Aouvhh27ZLmI2PGwCczHfTtXyvDUYWi6tC00t5EJrruFpXKuNGx\nWkU48net6tuP6D928tZ1Z8uXt2cPGDwIDmT435bNIt1q1YCb4mSgqEi+H9688w4UFkLnLvD0FDj/\nPPj0E1i3VvyMAvDCpleZ+c8cpnSeRO/TekCLFhInZmcfFY3QdY+5fDWieh3Nf0ybNtCrF8THn+gj\nUShqMTYbJMbC6U0gIUZ+JAuLJQOosEgygNydPe44cxzXnjaYSb++xIK9S323Y7fDiFHw/Rp4ZBL8\nvRUG9YcH7/MfRIFHOEpKlf04ShQNa5qU3B3MlABIoagoLt39qKBopOtV7qm1P3s/g2YNonFUY2Z1\neh2bJUCRfH6BmP/VV6KR4vhgs0G3btCug4WQOiEn+nAUipMDh92/GbbZOa08Qt3fRT8DdxZHCKNe\nWEbvx5rzeO9w9NWroF9fOHig9HYsFtlnSQsAhaKmoetQ7PIVcHJypENInz4wew4sXQYNG8Gtt0Be\nXsDStG92LefBNY8x7IzBPNj+HpnY8gzPAmZ2km74DmBXE2q1aKRQKKoRVqu0Vj61kWQfJcRKCVt4\nKFisUFSMVuzi3U7P0q5BG0atuZ2tmf+W3k5oGIwbD6vWwoSbYNYMuOv2wEbZdpsIQyEBTFg1TYKt\n/elVky1SVCzlSoragcvlflRwxLXYCQerrqytwFnAoFmDyCrMYkHvz6nvCgu8bXP0WIlGiuNNRFhw\nN7MKhaJ8bFaJWUr+tusBOqeVxGKRDPAAsU7dkLrMGjKblzvbuHVCY4xt26B/Pzh4sPTCdivkF1Z8\nwEShqE74+y58/hlkHobb75D3nS6CFd/Bhx/ByFFw6WWlVvn38DauWXId58a25sMr3vLYj51+umeh\nBLdoZCjRSKFQKMpH02S0KzoKYutDo3gRkk5tDBaNMN3OvEvfJ8IWTv/vrudwYab/7URESJe1B/4P\nFi2A22+RFNNA+ywLm1Vu+velHnsAlJUDGYdUvX9tQa9kppHTJSWbFRWb/GAYBjd/dTMbkjfw2cDP\naG1v6j6uAMeUbopGDY553wpFmZRM+VcoFJVH0yRjutR1Qwv+u2YOoPnLWALOqN+Sab0/5J0GO3nu\nrg4Y//wDA/pJx6iSx2KxSMas6qamqAoqcx4ZxrGdf0XFvllGTie89SZ0vFAeJhYLDBkK/3tH7j+8\nyCrMov+CYdgtNub3nUEEITIwCBAeDk2bymuzPK0s0/oTSPU7IoVCofCHww5NEkCDxo44vrz0Pfbk\nJjNs1UScehkXhJsmwqOT4ZslMPFGqUGuDCF2d3e1tMoLR4YBmdnyOjOrcttQ1Cxcugg0Fc1Sc7ok\nOKmCYPuNjW8w9depTOo2iYGn9xHvMIsl8DFlpMuz8jRSKBSKmoXDUdpLqDwTbG8sFsnwLuPa0+e0\nXkzpPImHQtcwZ9IQ+OsvGNgfDpfIojYzn47kSNZRNWoIoahhGIbYRFT0HHK55Nyr7D6Lnb7fnYUL\nxLj6jjuC2oRu6Iz8ehzbM3cyp8/nnBLeSAbGvTMCW7SU58QEmVaR7+t/SPU7IoVCoQhEiAOaJpKf\nBxF723Jn/adZnrKa+39+uuz1rr8BnnwaViyHG8dBQX7l919QWHnhqNBt9B0aAoezVdp2bcAc8a1o\nZllxsaxbfGznyIqdK7h76d0MaDWAx7o9Brluby5NC5zFlOH2qFDlaQqFQlGzMMvQzBtS8ya0IpkL\nIQ7JTAoQo2zfAXFb7qFjyGCGFU3jpxfvgT/+gFEjSt/UWy1SapOXD9m5Ku5RVA7DkOy3iopGulv4\nqYxg6dJlfbMawTDgtdeg+enQq3dQm3hs7ZMs3vk1r13yPN3iO8kAeHio27TeqxN0eDg0iJF9WMsx\nrT9BKNFIoVDUKJavdnDRNQkcPmjQN2IoXQrH8srW9/hk+5yyVxw1Gp59AVavgvHHIByFOiRTY18l\nhKNst7GxxT3CUMVGx4pqiMsl/++Kij9FxRI0BPLiCoIdh3YwZPYQWsW04tMBn2LRLDLia7WUnbJ9\nwC0a1atX6X0rFAqF4gRgcYs0ZnmZroO1gv4omgaRYXJTW+Jm+9134ZaJkJmp0Svrf0QcOZdLMt8i\nZdI9sGaNZGL42555k3wkR5WrKSqOYci5XOFMI7fwE6DcskycTtC81vthDWz+BW67Lahyz1n/zGHK\nhhe4ofV13Hz2WOkqGBku34cQu+ez3H0PLPnGbSCvV0s/I1CikUKhqEEUFcHo0fDqOyFcOjqBLhcb\nLB3+IK30i5mw9gE2ZPxS9gaGDYcXXoYf18AN10O+H+Ho779gwjhY9k3g7YTYIN8tHAV7U28YkJnj\nuRjYrdKVTaVrn9wUF4tIU9EgucgpI8aFAXy4yiGrMIt+M/uhaRoLrllAVEiUHEN+gbtkAE9NvTeG\n4emGE61EI4VCoahxeGcxVLYTk83dJMSrjPmvv2D+fJg5E+65ByY9FM7S4TMpzg+hW8hsXK1awmOP\nBfaPtFnlepidVyV+fYpahGF4HhXB5QRDl0dFKSryFYdefx1iYmD4iHJX/TltM2OX3kznRp1465IX\n0DQLREV4MoisVvEuMgxo0ADOP1+m64Z896ohSjRSKBQ1hrVrxS+uWzekw8dpjQmLb8AnbV+nvhbH\nwO9vIDk3peyNDB4CL7wCa3+AG67zCEeFhfDSC9C3FyxfCnfcCn/+4X8bmibCUUER7EoWc+vyLmQF\n7i4iZp2y1SrBWG4lM54UNQOny/2/rqBoVFzsFo0qnmnk0l2MnDuSfw78w+whs2lev7nM8C5N0zT/\nJXOGIYam0dHVNnBRKBQKRRl4i0RmuUtlCAv1bANpENWvn28S6kWtmnBNwTR25e7lsd7hsGsnvPde\n4G2aZXI5uWrQTBE8lS1Pc+qApeKZRrrbHsA8X//+C5Z+AxNuhLCwMldNzU1jwIJriAlrwJd9puHA\nBnUifEtEj2YEHoP/2H9M9TwqhUKh8IOmlfh9tVohrgE7j7TmLusnZBfnMuC7ceQ7yxFiBl8NL70K\n69fB9aNhzWq4qge8+Rr0GwDLvpOoaMI4/61kzYMJscsxJKdDyoGyy9WyckvXKFstKtvoZMcMOvyk\n+QfE7LhmtcpIVwXPj0e/f5TF/y7mtZ6vcdmpXq1fs3M8wYjF4j/TyKXD4UOqc5pCoVDUVKzujB5d\nP7abUNMU232t0Ch9jwvQqOgiJsS+zNNRv/LPeU3g+edKd1PzxuxIm5ev4h9FcBi4y9Mqso4Bugus\nWvADd6b5dckB3ffeg9BQGD++zNULnYUMWjiCQwWHWdj/C+Ic9SEsxH85W4jdV8wyDECrlp3TQIlG\nCoWiBnHRRbB/P6xY4ZmWmwvPveqg+RmXMK33h/x8aAvXr7kLo7xuVQMHi3C0cQOMHgEFBTD1c5nW\noiW884GU6dxyY9klaFaLpHBn58Du/ZJRVBLDkGwke4mLhs0qXR0qWYKkqAE43Z5GELwHltPlNi7V\n3LX4wadVT98ynWd+eIYbL7iRie0nema4XJCT7zFJtWj+RSNdl2BfiUYKhUJRcwlxuK85x3gTetQU\nW+fy7rBoMRzwGkvbuRPWrYen+ozl9vNvZsiFSRhHMuGF58vers0q2doq/lEEgxkHVaSs0VuEcZaz\nnsslImZmtsTrTpcnY8/phHlzoXdvMasOuDuDm1bcwbqUDXza8z3Oiz1HjiE0xP8Kdhs+KphueDoO\nVkOUaKRQKGoMdjt8/jkMGwbDh8Pdd0vTgXbtYOBAjX5th/H0ZVOYuXcxT295XQKSsm64BwyC/70P\nd9wFS1dAt0s8885tA888DxvWw1OPl31gmiaBla7D3pTSQVB+oVzoSgZuZpnQ4awK/R0UNQTDkEBE\n00QEKi9oMfEWl7QA4o4fNiZvZNzCcXRt1pXXe72O5h145BV6tmc+O12lR3l1d6ZRA9U5TaFQKGos\ndhvoHHsnJk2DiDBwuWh1WjHXjXAycbyTN19xMuUpnXHj4IH7JTn7pW7PkNDxMj5uC/p778COHWVv\n126TjI4gr3GKWoyue4yig17HAAwZJCtr0M4c2C0oku+Lw+4r3qxcKVUHVw8pc3ev/PImU//8nEkX\nPsTglgM83ZIDibYWiyfrzvyMdnvwn+8/RolGCoWiRnHppfDvv/IcFwdz58L773t+kx/o/CAjzxnJ\nI7+/xLysH8RQuKy01Ct7wJ33QERE6XkDB8O4CfDpVPhiZvkHZ7fJRSYp1TcIysoJHLQ5bNJNRAVN\nJx+GAbOmw5uvy/uKZBqZWo5h+BiRBmJf1j76z+xPQmQCc4bMwWF1+C6QlePJeALP+VjymFR5mkKh\nUNR8rBZ5VIU3nd0G0XWgThTXjI/gmdfDsUeHcnYrnVkzDXr1ksVsFhuzrvqED/s3I19zkvvwfWVv\nV9PkpjknT5WpKcpGN8WfiohGOuAenC3LD8mli8BqxvAl+XIO1KkD3a8IuKuvdn7Dvav+j8Et+vNY\np4fcpt1IJUJZOByez2QY0mGtmlJ9j0yhUCgCUL8+TJgADz4IF1zgO0/TND7o9wEdGnXg2m9v5rew\nA/LDXVRJUebB/4OLu8AjD8H8ueUvb7fJBSApVW72dd1Tmqbr8MC94qHkOWDJQjl4uHLHp6i+uHRY\nvBBmzXC/D1I0KnbCtdfAqy/Je3+G1V7kFuXSf2Z/cotyWTR8EbERsb4L6LoE5SU76Gha6ewnpxMy\nM5VopFAoFDUZ03exqtp3W91ZEXYbzc+0c+PtIQwYEUZcPafPzXi90Hp8NGYur3UNIWLJMgpfe0nK\n/wNhZo8EMTiiqMWYolFFuqD5CExllPqb3l/+KCyERQuhbz/xNPLDHwf+ZPiSsbSNa8MnPd/Dolkk\n3gux+fcy8sZuA838/mhgKWf5E4gSjRQKxUlHqC2U+cPmEx0aTb95V5PawD3iVolOVNhs8PY7cP4F\ncNft8NrL5Y+IhdjFByk5TVKvdUMCo7U/SsbSpEd8s58cdqmjzisjsFLUPFw6HMiA9DR5HWxQnF8A\nv/4CP22UIKkMzwfd0BkzfwybUzYzY/AMWse19rO9QjlnS46gmeVz3hw8JNNUeZpCoVDUbMJCq040\n8keIAyLCZaDDKy46o35LOj71Kd+fAiGPTsJocw78721Pt9qSlHOdUyhE2KlgFzTTHgA82Ub+KHYG\nFo2WL4OsLGmg44eMvAz6zh9KpD2CBf1nEWF3Vy3oRkCRyQer1dMsxYJvRng1Q4lGCoXipCQxKpGF\nwxdyIO8AA+YOIb9htAQ4BRXvRkWduvDpdBh0Nbz6Mtx9h4w+lIXDLjfrqQc8F61pn8kFYtdOWDjf\ns6ymyfTUAxWr11ZUb3SXmKkXF0vJV7AliMn7RFTcvVuCiTLEzskrJ/PlX1/y4pUvclXLq/wv5K9z\nn0lJISs9TZ5VppFCoVDUbEzfxONJqEM8j4p8haPLz7qKP6e+wOWjYVcDixgfnXM2vPdu6RjMapWM\nWhX/KAJheGUaBRvDu7wakeBnkMyk2BnYd2jOHGjQAC65pNSsQmchgxaNIDU3jfn9ZtI4qpFnv3a7\np/FIeYQ45BisAcrjqglKNFIoFCct5yeez+cDP2dD8gauXzIBo3E8RIbJTXhFhSOHA158Be6+T8rU\nrh0Bh8soKTNTw3VDfIvSUmH5Uhh7A7Q6E954zTfbyG6T9uqZ2ZX7sIrqR26ejFABZKQHLxrt3iPP\nKftFcCryf77O2DKDJ1c/ybi247jrwrv8b8swIDvXt3Pfsm/gjy3yumRnwLR0eVaikUKhUCiCITQE\nIkJLZRzdev7NtBo4nuZXJ/PVm3fCGWfAvffAB+/7rq9pQfv3KWohhiFikSmoBBO/ezciAclS8teM\nxHCXrfkTa3Jy4OslMGBgKW8wwzC4ecWd/JC8jqk936FDYjvPTJcOYQE6pvnDzAZ0HMeswCpAiUYK\nheKkZuCZA3n28meZ+cdMnvjhKWgYB1Hhlcs40jS47Q547U347Vfo2R0WLQi8HVM40jSYNVMuYCNH\nwZ13w+5dsGC+7/IOO2QcVqbYJwupqZ7XaallG7KbGAbs3et5vX+fBDQlRmDXJq1l7IKxdG3Wlbev\netu3U5o3hUWeriMgQdDtt8Abr8oIXEmvr4wMeW7QwKcTrEKhUCgUAQkNkRimRDbHa5e+wJXNLmfA\noTdZ+db90KMn3H8frF7lu77VInGZQlGSkjF2sKIRXpl2Fk2yv0vi0iXW8RdDfb1ESiqvLl2a9vxP\nr/Dxn5/x2IUPMuwMr/kuXTKMgs0yAsm0swfhf3SCUaKRQqE46bn/4vu57rzrmLxqMjP+nAWJsVAn\nsnLCEUC/ATBnHsTHyw34qGtgx/bAyzudMHMadO4Kp5wKV/SAM8+CN1/1FRLMG/v0g/4vkqq7SM1i\nf4rndXpacKOoLh32J3ve794ttfbFnnV3Ht7JgJkDaFK3CXOHzi3dKc2b3BIeEt99K6WV+/bJ+VYy\n0+iAWzSKrifPgVK2FQqFQqEw0TQID5UuVF6xitlRrUV0cwYvGcOOlx6B00+H0dfCrl2e9S0WGTCr\nSHcsRe3AKPE6mFi4pH+RpomgWXLdskyw58yBhg2h00W+k/+dx4M/PMbwM4YwudPDMtGle0osw8Mq\nVmamaVLiWRGh6QSgokGFQnHSo2ka7/Z5l67NujJ2wVjWJW+AxBj/wpFhyI9/eYHLOefCvEXwxBTY\nsgV6XQEvPCclZiVZ+T2kpEiWEUhwdOfdIggsmOe7rMMm5US5+RJAZeVCSjps2yueR4oTR2EFRUbv\nTKPUFBGNylvf6ZKyNIc7tXnvbgmS3OJiZkEmfab3wWW4+GrEVzQIL6eMLDvXNxBZvEie9+2Tkbfi\nEkLWAfc5Vq+erFeN6+sVCoVCUY2wWiHUXmqAJDo0msUD5qABvVeMJfOT9+WmfvgwyHaX5JvXmpID\nGQqFmTXk874c9BLeR5rmX3ByBjDBPnwYvl0Ogwb7DJ5tTNnEtV+P56KGF/LRlW+jOV0iFmlAZDhE\nR1XOfN5evf2MQIlGCoWiluCwOvhy6Jc0qduEfjP7sfPIbmgYC3XdwpH5ME2Hna7yy4msVrh2DKxY\nBX37w9tvwB23ll5v+mcQFw+XX+GZdkUPOOtsKRPyXl7TpHY6KRV2JMH+dMjOk9TtIzlirq347zEM\nSDlQsQ53pmhkt0Oa22C6PDHS6YT9+6FlS4iKEmERoNhJsauYIbOHsP3QduYOnUvLBi3L31ZBkZw7\nIMH5qu8hIgKyjkB2Frh8PSg4cBAiI8HuKFXDr1AoFApFmYSG+s2MPi36VOb3n8nurD303/IQRR99\nAP/8AzeO95Rf2yyVzwBXnLyUyg4KUjTyJ8KUXDeQCfaihSJgXj3k6KS9WUn0WzCUxMgE5vebQSh2\nKcmMjoK6UWJofRJnZ5+8n0yhUChKEBMew5IRS9ANnd7TenOo4LCUqsXVh/gG0DQRWjSF5k2gaQK4\nyui24E1sLLz0KjwyCb5ZAg8/4LnI7UuSTKNrhot4YKJpcMfdsGePGGt7Y7NKR5IQuzw77HLjb7VA\nmp/SNRPT0E9R9RQ7IS9fRpSCxexE1qKlCEga5Z9PLhckJ0OjRtC0GezZDRYNo6CQW5bcwrc7v+X9\nvu/T7ZRu5e/fFBjNwOnbZZIJd81IeZ+cLCNvppBlGNLtrX59eW2v3qnSCoVCoahmWC1iAlwyixXo\n3OgipvZ4h9XJP3JD8RyMp5+BxYvh7bdkAYtFroGqRE3hTcmMoWBEI2cg0cjr3DIrC/wt9+UcOPU0\naNsWgKzCLK6aN5gCVyFfDZhDbEh9OV8jwqq9F1FVoUQjhUJRq2jRoAXzh81nV+YuBs0aRKGrCBpE\nQ706Uo9v/viHhUKjOAl8gg1gxo2H2++EL2bBlCfkgjRjulyQho0ovfwVV8LZraWTWsmUbH+tcm1W\nyC+QkrWSGAYcyIS9KWWP0hkGHM5SI3kVJa9Ass8qYtSZlg5160LTplKeuBU6eAAAIABJREFUZmjl\ni0aFRZCSDI0aQ7NTRFS0WHjh59d4/5f3ebjLw4w5b0xw+8/K9Wo3i5SmNWwI/frL+6S9vkKWYcCh\nQ9I5TTdUppFCoVAoKk5oiFxb/MQZw1sN5cmLHuWzv2bw+LmHoH0H+PJLzwKa5r/MX1F78c5c07Tg\nBkddLol/vvgCtnt5jnrH83oJE2zDgN9+g4f/D1atgsGDQdModhUzdPFo/j78L1/2/Zwz658h24kM\nr/YlZVWJEo0UCkWto0uzLnzc/2NW7VnF+EXjMQIJKJHhUsJWXBx8Bs+d98B118OH78MrL8IXM+Gy\n7nKzXhJNg3vug7174N3/lb9tTRPPo/SDpcWHzGw4cNhdYldGwJVfINlKZS2jKE1OnvztC4IsDzQM\nMZWOjYOEROmehlG+AJmeDnl5IhqdcgrsS2LWzvk88PMUrml9Dfde8AS33SbJQGFh0tRj584A+8/N\n8wg/WUdgzSro1UdELBBfIwOP/4Suw2G3aGQYlavLVygUCkXtxmKRgbcAzR8e7ng/1509isc3PMvv\nrWPh182QlSUzbVaxCVADWwoT3fCIMxrBDeTqLsjNhfHj4OWXZJpFk5J8E5fbBDsjHV58ATq2hy4X\nw//ehl69YeJEDMPg5hV3snTPt7xz+Wuc5rqUyY84Of28MGITrdx3nzRYqw0o0UihUNRKRpwzgicv\nfZLPfv+MySsnB16wTiQkxEgQE0xKrKbBo5Nh8BDJIDqQ4THA9sell0PvPuJtVFYHNhOrVS50h7I8\n07JyIe2AlLOZ7wNxJFtKrXLyyt+XQtB1MSZ32KU8LVgTxgMZEBMD8QnS6j4nu/wOarv2yHPDhlKe\n5nTy2Df30jW2Ax9f9SGDB1nIzpbBsJQUuOAC6NYNMjNLbKegUI7TzDRatlTEz6v6QN1o8S3alyTz\nTAHSpUumUQO3uXY17+ShUCgUimpKqCNgVoimabzb/XUua9KNe41v5Bq0bp05U2ItNbClMPH2Jwom\n08g0wf7zD3ne9JNnXafXuqYJ9tjr4InHpQHIK6/Cth0wYybExDJlw/N8+McnPNrxAfoljuH+u520\nbG1n858ONmwQ28mRI4/DZ66GKNFIoVDUWh7u8jBjzxvLE6uf4MNfPgy8YN0o8TwqKhbBpTwsFnj2\nBeg/QLqsdfHyn/FjEMnkJyRt5MH7g8toctjhYKYcT16BmGXb7bJfh02EIX/ChssFWXniN3AkR43k\nBYtpzGmxAEZw54BLl05ksXGQmCjT0tPKX3evWzRq1Jg9DSTTp3N+LPM6v8PWzTaSkuCjj6BJE4iO\nhocegi5d4NNPS2wnN9+3Te1XiyR76by2Ejg1agxJbtHIPCaXmWlUXwKpWlKnr1AoFIoqRtM82UbF\nxXJ98Yo5HFYHX/adxsFzmlNohYxlXt6ONotcw3LzVJyiAEOHO2+DBx9wd0Er55zQDbED+P13ef/3\n3zKyZgpO5vpOJxQUiGB5x52wdDmMu+HowNmnW6fz6NonufbM4Tx+0SMsmq9z8cUw4oYwouponHYa\nTJsG69fDX38dx89fTVCikUKhqLVomsa7fd6lR/Me3Lj4RpZsWxJoQahfF5o1FOEgmO4eNhu8+iYs\n+Mr35rvIKQbF3uvHxsHDj8GmjTBjWvkHbnH7HaUekC5rNqunQ5bFIsGZvy5f2e4AzGYVoaBQtbYN\nilyv3GODiolGMTEQEyfT0tPKbies61IyBqTXc3DNrucAeK7BCOqHRLN3p5NOnUo35+jcGbZu9Zpg\nGJJtZhpZZx6GH9ZIlpE5WtekqWQaWTSPufeRI3J89d2ZRko0UigUCkVlCbHLoFt4mFxrip3ycGdt\nR4dGM2/YAjY3dZD89Rfsy06W9SwWKY8uLJYBrvI62SpObnQDfvgBVq10i0Z62TG4oQOGRzQC+OUX\n97ru7RmGZB1t3ixxz0UX+2ziu70rGbdsIpc16cYHV76FpmlkpLho3CrcJwhzOKBDByUaKRQKxUmP\n3Wpn9pDZtElow5DZQ9i0f1PghcNC4JRGEB0pwlEwndW8TfLMLKM6kaW7cF09FC7uDM9OgZT95W/X\nYRMxw6KVLiOyaOJx5I1hQGaWjOCZ5KoStaMEyvAyDMjO9e0kFkwHtexsyM2BmFioEy3T0tL8dpQ5\nitMF+5MxwsK46pe72BKSiR7iICYtGwxo0czJunWlD/WHH+DMM72345RjNAObpd/ItD79PMs0biyi\nkYZHBEtPl+cGDSSwsqoQQaFQKBSVRHPHJ6EhEveYDUeczqM3/U3rNOGUPqM4J7mYIdP6kVmQ6VnX\nbgMMOJJberBNUXvQdYlP3INqUE62kdkRbcvvcP4F8vqnjb7bMzOONqyXaR07Hp29JeMPBi0ayRn1\nWvBl32k4rA5w6TRItPLdGrvProqLYeNGaNWqij5rNUZFhAqFotYTFRLFVyO+Ii4ijqumX8XOw/6c\nhd1YLRAfA43jZbSioCh4k+wiJ0RFiEeSpvma+WkaPP2cBFOPPuy5IBqGXCjX/egrUmmaiFj+zIrt\nNvEs8l6+qFiO1cwesVtFWKopQZhhBC67O1Z0HXbv9++h4HT5CjAWzdPKvixSU+U5JgYS3Sbo6Wll\nj5g6Xej797E3WmNz5lZmdn4DS9NTYM9usGic1byIxo1h3Dg5JY4cgWefhTVrYPRor+2YWWamYPnV\nYvFHan2OZ5kmTcUk8khWadGoXn15Vp5GCoVCoagqLBYRkMJD5brjvp4n9BiM1YC437YzcOFwCp1e\n11irVeKVvHyJWfILg4+5FCcHWdniC3nkiDzwY/PgjVOXWOvPPyUVu1Ur+Oknz3xd98Tf69bJ/PoS\n9+zJ2kvPuQOJtEewZOBcokOjj67T9+pQ5s2D11+Xw9m1S/yMOnaEs846Ph+9OqFEI4VCoQASIhP4\nZuQ3OHUnPT/vSUZuRuCFNU3En9OaQGw9dyv2cgIZw5CU2QbRcjMe16B0qVLTZnD3fbBiOdx1G4wY\nCm1bQ5cLYcQweC+IDmvm8RkG5HiVVWXlSFaJKSRYLBK0BZM1Ux04dAT2ZwRXGlZRCoqkq1z6wdKB\nSEkBxmqBwiBEoxQv0SgyQgyIUlPkXAkQ7OjFxezZtpGtEXm8d8EU+jS9Ujqd7d0NFgtaURHz50NE\nBJxzDsTHSxy0cqX4Nx4lO8+TJXTwIKz9wbc0DSTTCGD/Ps+oryka1a8v50ctaiWrUCgUiv+I0BAI\ncXgaQ7TvAA4Hz9CdlfvWcN3SG9GNEoNqDrtc1/ILRDzKyw+ui5aiZuMdm4BkSBuULRrpLti+DYqK\n4Nw2cn5t+sntTYkMqDqdgAEbN0CnTgAczD9Ijy/7k+vM45tB82hap4l7e9K9Lb6xjRUr4NtvJUxq\n315CtOnTj9eHr14ck2ikaVp9TdOWa5q2zf1cL8ByuzVN26Jp2q+appVR+6FQKBQnjjNizmDR8EUk\nZSVx1fSryCnKKXsFq0VEoOZNILa+BECBOn4UOSEqUjqKANSNhJCQ0iLI2HGSTvvN19J6vXcfeOoZ\n6NoN3nzd3bo9CKwWT4marstr76wkUxCoyi5qhhF8S/qKkF8AGYfl9fHoqJKXL6OZOfm+/kUgpWkW\nL/HEYgmug1pKijzXj3FnpyVIeRoEDHQfWPUwUelHiG/ehuubDxVxsUkz2LNHBL+iYurUgTffhMOH\noSBP58uPcmgelyt/o2KnbDs3z5MltPRrCZC8S9MAGruDITMAc+mQ7hZK69XzLcdTVEtUDKZQKGok\nmgYRYXJtdDqlEUj79py1NZ1nOz/BzH/mcPfKBzFKXmfNkjWbVWKNI1lyjS4ucU3WdblOZ+eqph81\nHcOQLG2TpH2e6YFwuaQ0DeDcc0TdOXQIdu4EzeLORHLBP/9I5lLHTuQW59Jn/hB2Z+1lYf9ZtI45\n23d7YSGgaZx1FixcKHrUgQPw4oty+tYGjjXT6EFghWEYLYAV7veBuNQwjPMMw2h3jPtUKBSK48ZF\nTS7ii6u/4JeUXxg0a5BvmnQgrFYRj05rIqNnJYUNM8soJtozTdMgoUHpzBObDWbPgz//hfmLpWRt\n5LXwxBQJrl54LvBxLPvGc3G1Wd1CgrvDmksv7aBc1SVqOXmwJ0CZV2VxuSTDyGqR48/LL3+dipLj\nFlnsNkg76MkY03URkUqKbcGYYZviXoMYOe64eMk00jS/Xlgvr3uZtze8QUw+tD2np4hEYaFSRlZQ\nABnp8j80BafiYjFB358OyemwJwV2JsG2PXJ8pig4fx6c1hzOLJE7bWYa7dsn+3K54IBbNKpbT85D\nRXVHxWAKhaJmommShYu7VL9LV/jtN+5vMZY7z7+F1za/zTMbXwy8rt0u1ymzK2xmtsQ8ObnyOjvX\nk1HiDMJ/UlE9KZlplLRXnvUAcauuy7wtW0TNadES2rkvez/9JIOALvc5sV78jIo7tmfY4jFsTN3E\n9N4f0bVxZ9/9G0imWy3nWEWj/sAn7tefAAOOcXsKhUJxwrmqRV8ePOsDlu9czvAvRuPSgww4bFZo\nnCDtFLw7k5lZRiEO3+XDQqWzSMkSMYuldOeqZqfAuPHw5Wz4dXPpfb//Ltx4Azw+Sd6bokGWO4Ay\ns2WcTo+vTlWWqDld0s3NpZc24a4shiEiTrHTPbpo8S25qwqcLrfXk8XdVa7Yc/yFRYDhv0yrvL9Z\napqsF11P/u8JiW6fI6NUptG036dxz7J7mBDRDQCtcWMJUkJD5P8Okm0E8r/LzoVdyXLcoQ7PI8Qh\n3WpC3MHNviT4aQMMHFz6M9SpK499SZ6/Q0aGZL+Fhfn3ylJUN1QMplAoai5WC0SFi7jTpQvoOtr6\n9TzV8Rl6xF7Dwz8+zv9+/Sjw+pomsZLD5i5dK5RmEzaru5zN6pmuqJkYhscjEtwDXVpg0cgwAA1+\n/w3OOlvOgVZnQmSkmGFrGugAYoJtJCQwYduLfLXrG9667GUGtejvuz2nS+KrkoOutZBj/QvEG4bh\nzsEnFYgPsJwBfKtp2s+apk04xn0qFArFceOff6B1a5g36TpO3/kC87Z9wWUv3F46TToQNis0iZeb\nbrOMqWSWkTex9QAtOGPHibdBbBw8/pjv8gvmwdNPQlQd+HaZtFgHySQ6nCWZNKYIcN0omHijvK6q\nEjXDgPRDIoaEhojoEkxnufLIypHUclMEMUWuqhw1NMvpzL+Fww4HDss+cvPl6gXiY2SOcEH5olF6\nughGdruIOfHxcPCAbMfrb7Pon0WMmT+GS065hOfirpWJDRtJ9k+oQ3yuQMywNQ0yDsG+NAmEQ+yl\nxSBN880yAhgw0HcZw5C/Y5MmXuVpLvE/qu/unKZEo5qAisEUCkXNxmaTQa127SEkhD3TVtOvj4WG\nq/9HwyM9mLjiTl7+dn752/EuXfO+Llrdg0FVEZMo/nsMJIPeaoVTToG9e0s3kvFGd8fcW7ZAm3Nl\nmtUKF1wgvkZe2zXWr+O30yKYunUaj134IDe1ucHP/g2PrUQtp1zRSNO0bzVN+8PPw0eKM+SOKtBd\nVWfDMM4DegG3aJrWtYz9TdA0bZOmaZsyMsowolUoFIoqRtdh4EC44w744w/Y9sm9TDj7PlYXvM24\nzx4PfkM2GzRJkAtVXoH/LCMTu02Eo8IgfHIiI+GBhyTTaP5cmfbDGrjvbriwE3zymRRaL1oo86xW\nTxmVpsEfW+DHH0RY2r/fvX/rsdf85+RJZ7MQuwR/hiEZTsdCYRGkHhQRxwwAzeeqLH/LzReBxsRi\nkVGog5nyGUxvoBefh57doSBfPmN53k0Z6RAbK69D7BCX4J6ecVT0Wrl7JUNmD6FtYlsWDluAI9k9\nmtawEVhtcm4kNpTzyfQ1ysmXAKZkJlpJDAPmfQntO3r8i0ycLjnfGjX2tLAtdoqoVd/snKZEo+rA\nfxmDqfhLoVCcEKw2cDgoOLc9hd+u4a234aP37Wx75DNaR3bg3l+v5+vtKyu/fU2TzFxFzcMsT4uL\nE9fpo5lGAUQjl0sGwzIz4ZxzPdPbtxchKS9PYqmU/Wh79/JxnR3cdt5NTO70sP9t2e3lx1u1hHJF\nI8MwuhuG0drPYwGQpmlaIoD7OT3ANpLdz+nAPKBDGft7zzCMdoZhtIs1A26FQqH4D9iwQTSDCRM8\n+sQ7g5+jvW0sH+96nFfXvxr8xuw2aJooNfuBsoxM6tVxt6ANYiRs4GDpBvHcM9L14aYbxLPm3Q+h\n7QXiXTPnC8/yDps8AD6dKuVHhuERnUxj58qWqJllaXab549mt0q3s8oIUYYh6+7eL+KM1c9lKr+g\ncsfqb185eaUFkhCbZGgVFcv+i4pg7mwJNrZulWlliUa6Lg6JMe5rmMMOiYnyOj0VnE427d9E3xl9\naV6/OV+P/JooWzjsT5ZjiYmR/5nZnrhRY8k0cthFMAqmq9nvv8HOHTBwUOl5Ll3+X40bS3ClISWU\nBw9CgwbulH+Vil0d+C9jMBV/KRSKE4LdBrrBH/W60iLvN1rFZwIQbg9n9ZjZ1HOezuDF17Ah5ady\nNhQAm1VEo2AyuhXVC12XJiLx8eLxmLRXYpaAopEuo74gsbJJ+w5S3v/br2C38c2cpwGI7taDVy99\nHs1fXOXSxQBbARx7edpCYIz79RhgQckFNE2L0DQtynwNXAn8cYz7VSgUiionM1OuS97XDk3TuO2U\n92h0ZDB3Lb2L939+P/gN2m3QLDFwlpFnJ5AYKyJGeUGNxQKTnpB03WuuhrrRMPUzqFNH5l89VASD\nf/+R91arrHP4MCyYD0OGSfbJnC9kf+aHza5EZpB3WZrNayTGzHDKq6C4k18oYlHaIRGe/JVI2Syl\nO5xVlmKnPCx+SrzMlvOaBt+vkM4bIAGHxSIiS1lBy4EMT6aR1QqNGsrrtDS2pv9Jz897EhMew7JR\ny4gJjxHxbX+yZBZpFo/posMOzZrB3j0V+2zz54q31lV9fKeb//NQBzRsDPn5kHlIhLFDh6Q8DUON\nrNUMVAymUChqPjYLGAY7ErugYcC6tUdn1Qutx5jChdS1xNFz7kB+y9hS8e1r2tEOpIoahq5LvBuf\nIANdKSki/hhlZBpt+V3itLO9OqB5mWF/tnUG/349jfwQK4+On4ZF8yOHuHSP16UCOHbR6FngCk3T\ntgHd3e/RNK2hpmlL3MvEAz9omvYbsBH4yjCMb45xvwqFQlHldOoEv/wCu3Z5phkGTPvMxv+dMZ1e\np/fixsU3Mn3L9KrfucMuZWrBtHM//wIYOkxao3/yuZgsm/QbINkq3tlGALOmQ1EhXDsGBl8Nu3bC\nr7+4922DA5kVK/syDClry8r2eA55Y9EkYygYdF1K0fbsd7ffLcN00GoVcakqRgzNbKEjmZJl443D\n5vlcc2ZL97OYWBHkTDEpUAc1XZdSr5gY9zFboHFTAA4m/c2VS4Zis9hYfu1yGtVpJMuYolGjRlKT\nb4pGIXYZXdu9O/jMreJiWLQALusuZtc+85xQJwJCQ6UMDiB5v5x3hw9JphFIEK+o7qgYTKFQ1Hws\nFtCg8aD2FFlCcK1cfXTWkSz4bU0Cc3ssJsoRyRVz+vL3oX8qvg/TELuqusUq/ht0d3lafLyUpxmG\n2CsYRun/pWFILPXHFmjRAsLDPfNi4+CUU0leuZCxS2+iV2okjo4XYXOEeu1Ll/jJFBfDw4LL7K4l\nHFNUaBjGQcMwLjcMo4U7hfqQe/p+wzB6u1/vNAyjjftxtmEYU6riwBUKhaKqiY6GKVOga1d4+WWY\nPh169YKcHBg72sGXQ7+k2yndGD1vNAv+LjWof+zUqyMXqaJy2rkDPPMC/LABTm/hOz0mBi69HObN\n9XRJc7ngs0+h00XQ8gzo3UdEgzmzZb7FIiJPSkb5Yozu7o62cx+kZki9t7+Lqt0mGUHBjOzl5MHh\nIyKQBDJg3r1LhK6jvkZVMGKYkyef+/ZbYVA/KPSTGZWRIZlGAwdBm/NENAKPmbQ/jmRJKVtsnGzf\nYoHYBughIcz76RPynQUsu3YZp9c/3bNOsVMCoUaN5b35d3A4oEkzyM6SbLFgWLNaRLCBg0vP0w2o\nEwmhds++kpOkTXF+vscIW2UaVXtUDKZQKE4KLBZAo1PXEPYmdCRpxhoWLYLZs2HsdeI12emMpnx7\n9SIsmoXuc/qy68juiu9DNzxxkaJmUOz0eBqZ/oz7kgCttGjkcsm033/39TNyk3xmY/SNG+hatw2n\n78vD2ulimWEY7gFbpHtsdJQ8HH4GRGsxaihRoVAovJg4EWbOFOuauXNh0CBYvlyuI2H2MBZes5B2\nDdsxdM5Qlu1YVrU71zRIiAH8lKmVHFWxWOSg/HH1ECmPWr1K3q9YLlksY8bK+6go6NFLDLNNocRh\nl1G4w1n+t6nrYg69PUnEIsMQv51A3jemuHMku+zPbBhw8EjpjifeJO0VUeeWmzzTyjOiLg/DEFPp\ngnxYv1bKv6Z+XHq5BfMkELl6qNTH79wBWe6/UaDMrBR3Q6sGDY76JSUXH2BPlIv6mQUsv+RTzo07\nx3edvHxJwW7UCNA8KdF2m28HtWCYP1cU0Esu9Z2uu9Otw0Nlu0dFo32SZQRihO3dgU2hUCgUiuOJ\nJtc8CwanjulCsyO/kzP1C/at2cm99xjcMlEWa1mvBcsHLyTfWcDlc/qQnL0/8DYLCmDZMkhK8kyz\nahLnKGoOGe7BzAR3eRrAXnfX15KiUbFLBtf27YM2bXxmLd/zHS9pa2mSBYu1kWi6Lg1kQLZvt4tQ\nFBaiBs0CoEQjhUKhKMHFF8MHH8CcOWKK7a3NRIVE8fXIrzkr9iz6z+zPtzu/rdqdO+wQHyOZNAVF\nIkwUFsn7YLNrLrlMbv7NErVPp0LDhnD5FZ5lrh4q2SvLvYSvEAdkHC4tyBQWiddQ+iEpWwoN8V/n\n/ewUeOVFr89ig0NZZWcvmZ8vUN14bi6Mv14Cgb+2iu+OtQp8jQrdppjr10k6cuMm8NbrvmVqhgFz\nZsF5bSWjq815Mv2PLWWbYae4u6A1iAH7/7N33/FR1OkDxz+zLZ2QBBIIvQoovUtXmqIiSBEQ7Ipi\nO+vZ6+/Us995KiqKDenSEREERKkWQJEivYZeAiTZ3ZnfH88Ou0k2jUBAfN6vF68ku7Mzs7Pea7/3\nzFOc7E7fzaVf9WRbnEkXoyZNEi7Kfk0sS2oiTTNQMmYFm3O7XNLTCAoXNDp6FL75Gq64SrKUQmX5\nID4uOJo4NkZKHLdtCwaNSifmH8BTSimlTjeXEywTZ48eGFFRDJh9E/8Y2YCLB1TC6HkF3HcP/PMR\n6v9vHCt39mTgrF289s927Jk/U26SWZb05vv6a7jtVqhZHfr0hgfuDx7D7rfoK8TQEXVuSAusp1JS\ngkGj7duAMOVp3ixYHWjZF5JpNH/b9/Sc3J+0erKWih4+Qm68Nm8uG/it4MAYlScNGimlVBElRCUw\ne/BsaiXW4sovr2TOxjmn9wDxsVAxRf5VSYXqlaB2FQko5VUSFcrjgZ69JMNo2VL4YSEMGpJ9Sljr\ni2Wi14RxwccchtyJ27VPAhiWBUfSJWDk88sdmLx6DU2bAsPfhXfeljtDINtapoyuz8vBo3lntpgm\nPHAvrF8H99wnjy1bIgGb4xnF601g321cMA9iYuD9EVJS9tbrwW1+WwVr10qADYKTOFYGmmHnNcJ3\nV+DuZ1IS+3xH6PxpZ7alb6dOrTbE7U+X5/whQaMDh2HDRvnd7jN0MtPICRUqyfUpTDPsr2dAZmb4\n0jSQfkYg/y1YSLBse0jQKDEh7xJBpZRS6kywv5MaNIAt22D+9/DWf6Q27fBhmDoVPv8M/vsfKvzn\nY174OpPXP0sj+cq+UL0aVEyF6lWhXx/4eib0vBq6dYf58yTryOZwwLHjxe9tZFmShaxOj3Cfh2XB\n7kDmdkqK3MEtWzYQNELKDW2mKZlGqwKN0htINvePOxfTY1IfqsVX4Y17ZsgE4dWr4aKLggNkDEvX\nPYWgQSOllDoFZaLLMGfInJOBo7mb5p6+nRsGxMVAbLRk9bgD49dTkiR4k9dix7KCwYg+/eWu27Ch\n4ImA/gOyb+t0Qq8+UsJm38kBSdHNzJJStLT9sGOPBDDyuwuzdw88+RhUryH9AiaENOF2u2DvgfB3\n9nx+KV/La99vvQ6zvobHn4I775Y+TEsWB4NRhQmg5eXoMQmSzZ8HF7eFuvVgwHUw6nPY8KdsM36s\nXLsrr5K/ExKkVGzFCnmtN48JamlpAOyLcXLp9GvYcHADU/tOIrlyPbnWlhlcbKYfl+uzR15DaoXs\nmT4OB0RFSrPzzZsLfl9fTZDMpMZNsj/u98tnYU/yMwy57hUqSir3fjvTKCF7cFEppZQ605wOCRqB\n/B/7xo3hxpvgrf9KAGnDJti+E/YflB6IO3bxy7QR9Lsukv/rVYZj/XpLP4Gx4+HPjfC/d+DmW6RX\n3w8/BI/jcso66Xgxs5W9Prkhpo21i8/nDz9t17IgbY/8nlJOflaqLOVp9vM2vwkY0s8oNRXKlOXH\nnYvpPrEXqTHl+PaaaSSXrhjMGLdL0yxLJtbmdUNUnaRXSCmlTlHZmLLMGTKHGok1uGLUFczbPO/M\nHjA6UoJJ4RplW1awnM2yoF49qHehBHSuvCo4FStU7z4S9Jj0VfbHPW4pUzt0REaz59W3yD7uPx+W\nhdn7I6B5Sxg9KhhMcTol9XfvgdyvPXoMsMJnGU2fBv95E/r2hxtvlkVkk6YSNEJelmemT0FME05k\nwLYtcseqQ0d5/L77ZdrGv16QbJ0pk+ROZegEsgYNgxPUIHzgavduLIeDS369m3WHNjDl2ilcUuNS\nWfT4fFIC5zPls9qxR4I5u3bIa8uVy37HyzAkc6xKlbzL03bvkiyv7p1lVHHvvrmvqdcv9fqhj0d4\nAplG2+FQ4PNJSNQ7bkoppUpWYIJaoYIwTifExdG4fX/ufXwqLzXLoGmDH9n94pPQvXuwNLt9e1k7\nzM7Rf9LllPXDqfZGtCwJOvlNbax9Ovh88lnkmoaGNMEGaYQNUKlTrudqAAAgAElEQVSirNsMI3um\nkdcr//2sWgkNGvL99h/oNuFqykUnM/eqSZSPDQSd7JK01oGgkd8va14tyS+QBo2UUqoY7MBRtYRq\n9BjV4/RmHOVkGJCcKF+sZo4v1yyvZCbFRgezevpdKz+H3JB9W/uLuUYNyUiZOD5Hk21DStEiIwr+\nIh0/FuZ+Cw8/CjVqwsBBsGUL/BhyZy/CBYfTs/chsiwpy8oZoLAsmDUTHvqHBIme/1fwHFq2kr5G\nhw/JY6d6pzAjSxYj8+fJ33bQKClJMprmfgsvPAuHDsE1fbO/tkFDaSq+b5/8HSaAd2znFvbFGGw4\nsZ3pvSfQpUYXWRCnpsoGaWmywNmxR96H0ynNqMsmg9uTuxeRJ9AMe0tIedrhQzBuDFx3LVzcQvpJ\nRUfDsy/AHcOyv97+bONisj8e4YHyqZCVKSWALhfExmnQSCmlVMkyApNGi5i506ZCa2b2nsj29J10\nGncZO9N3BZ+MjoY2bXMHjey+fscy8g765HcemVkSMHI68h6IoYTPV/A1yvJlz5S3WZZkYcfFSRsB\nkEwju7l56PZZPlnLrFvH5irxdJ/Yi4pxqczvPZ2KCZWD2d3du0vPz3btAsdAp6QVkgaNlFKqmJJj\nkpk7ZC7VE6pz+ReXM2P9jHy3nz8fbrxRMqnfe0+SdArN44ak+Oyj7LO8EgBILQsJ8cEv0uuGwDdz\ng714QLJsjmUEg059+sG6tfDrz9mPU5i7Ltu3w3NPSzDnhpvkscsul8ldoz7Pvi+XE3bvC57b8QzJ\n0gmdUrF9uzS9HnorVKkK730gdwltLVrJImLZMtlfzmbYpimBqILK1o4E+grN/04CXfYYV5B0+IqV\n4PNPJeunbbvsrz3Z12iF/MzKvhjacWQHi1d/ze4Yk5kdPuaSapcGn7T7Fe3ZLeeZ5Q2W5u3YIZPT\nTAsicixgIjxQsTLs3wdffgE3Xw/NG8PDD8gdt3vug7kLYOIUCRC6c7ze75eMsZwLI48nOEFt5QrJ\nMrKDWEoppVRJcrty3xArhLYVLmZmr4lsP7qT9mO6seXI1uCTXbrC+vUny7u9Ppg6DR5+xODZfzlY\n/O1xLHtd4vdLv8NDR6X0LFz5uWnK+sXtkqBRVh5l6kp4/fkHjSxLAkuGI3cAz7Jgd1qwNA2kGfaJ\nEzIcxb7upgmmH9asAb+fR49MpGp8Zeb1nUn56BS5AWp/xh06wuatkJwSmEpM/tn06iS9SkopdRqk\nxKYw7/p5XJR8EVePvpoJqyeE3e7NN2HIECnX79cPJk+GLl2y92ksUGK8fMn5/bJgcTqlabbTCTGR\ncrfONOXvWrWzvzbLBzFRkukCMmUrqQw881TR0qxNEx55QL50X3k9WA8eESnZObNnBRtigwR5vD7p\nRwASNHHYJV5eeO8d6NoJflwIjz4BU2ZI5k2oxo2lx9DiRcGeQnZW1bETsGmHBKZ27sl7EXf0GBw8\nApZPSt3sLCNbRCQ88qj83rtP7gDKRfXlva78VT6DkPG9Ww5tocPIDpQ6nEHFKg1pn9wi+2KkciA4\ntWePnHtocGjH9mAAJ2dPIY9bgmgAjz0iC6MbboLJ0+G7hXDfA1Ctevj3C1IKV7pU7sfdLqgUOKc/\n18vdNwNdQCmllCp5pxg0AmhXsQ1z+kxjf8YB2o3pyvqDgd6EXQNTY2d/g9+Ehx6CSZOgY0e4qL6D\nd9+xGP7qMQkUHT4qAQkDCTKkh2mYnZEpgQZ7gIdl6TS2/Ph9efd/BFnHWpYMYQkXNNqTBikha0F7\nzbJ9a3Cffj9Y8Nvc0QAcuqAK8/rOJCWqrKxnIjzBzyqUacmwEe1nVCh6lZRS6jRJik5izpA5NK/Q\nnH7j+/HZis+yPX/gADzzDHz/PdxzD1x7LcyYIRnUn38efp9hOZ2QnASZgRruiinBQIPDIb1rwmXb\nmKZ8caYkyaLHsmR6xDPPSabJxyMKPvb27fD2f6DrJVKC9vhTki4casAg+fIfPyb74xFuCRYdCZSq\nuV1yTgP7wcv/gjbtYPY8uG1o7mwZkIBOo0awdHFgwYbsZ9de2LZb3k9UhNwF3Hcw9+u9PtnW44Kl\nS6RvUfuOubfrcSW89Tbcfmfu52JioGYtuV7OwBSWzCzW7FtD24/bsu/4PuplJnEoqwazZsE77zuD\nmWQVUuWz25Mm52lnc5km7NwlmUYGwclpNpcLOnaCJ56GiZNh4WJ47EnJeiooI8w0JcAWF537ObcT\nygeynywr0PfKyH18pZRS6kxzGDLJ6hS1KN+Mef1mkuHLoN2Yrvy273f5vq5aFWbPZuH3ci9r+HC4\n/HK45hp46x0XM6Zb7NiNrDvcbllHuZ0SDAoNHPn9EjRyh3xHOhy5Mo5VCJ+Zf2DN6w+WJnp92QM7\nliU32VJSgo/Z683t22WoCECWjzF/fsWSGe9xNMpBz6RZPPNQWZ55ymTOQjcWhmRb5zwHu5+RKhQN\nGiml1GkUHxnPN9d9Q8eqHbl+0vUMXz785HM//ggtWkDlkBiLYcDgwTB7dhEPVCpGgkMVU4ITsU6e\nRGwwKBQqyweJpaShdnRUMLDU40q4tAu8/kr4ZsuWBVMnw7V9oF0reO3fkJgEr74B1w7MvX2NmlKy\nNvrL7HeX7NKnXfuCfy+YB8uXwVPPwAcfSeAkP61aw++/wZEj8h5374XDxyQgZU8di/TA/sOBRtsh\n72HX3kAqshPmfSelby1b5j6GYcBVVwfHseYU2gzbMPhpxWzafdwOr9/LwPTZRB48QkzVstSpYzB9\npkH37oE1ZWSkZE+FTqsDKTvLygzJNMoZNHJKhtXNt0LjpkVr2Jjlk5LFcCVnTqdELMuUlb8TkwJ3\n/HRpoJRSqoQ5QiaonaKGZeszv9/XOA0nHcdexk97foXOXWDBfH76MYPu3bJ/xZaOh4ZNnCxbHuZ7\nz+2SddKxE4Hm1xnBDCOblqjlzbKkbMzpzDuw5s2Sa2hnAoVeR9OSHpAp5eS5E5lQMbBG3Lb95Dp3\n+E/DGTDzJi7f7GFNQlfWr0ymf3+4uLXFY0+7efZZZJ2cq0+VodNii0BXhkopdZrFeGKYPnA6l9e6\nnKHTh/LCghewLIuEBNi9O/f31q5dUhlUJIYBqckyjj0nj1sCJ/6QuyqWJVksdplSUnwwDdww4Pn/\nky/Px/+Z/QS9XnnsnmHy5X3/Q7DgRxg7QcrQ8gpgDLwOtm6BHxZmf9xusmz38hn5kdSWDxpSuPfd\nsrUsKn5aFggUuSAyx+QLe5z8zr3B3k8HDksvJ/u48+dB64shMiqwGMwsOC0+0yvHbtBQJqDt2MG8\nA8voNPtaYhyRfNllAb+Nq4LTl0nyBWWoUsPJ1KkGpgnjxyMr1ZQUmXYWavt2+ZlaQRZB4YJG4VKr\nC2IGPvOEuPDPG4ZcQztYZZenaaq2UkqpkuZwSADhFEvUbHWT6rCg/yxiPbF0HHsZvzYqB8ePU3vf\nj+zbn3v7ffugVB5fk7ic0pMn/bisJ3LegNEStbyZFlhGMLCWqzzMBK8Zsn4zsje3Tj8q/1IC/Ycc\nhvRejI6Wfo7AS9+/yNDv/sHN0W0pvz+TDRW78uqr0L6dRdeuBlNnOHnrLdi1xykZYvb+7f3pTbJC\n0yullFJnQKQrkq/6f8XgBoN58rsnuXvm3bRo6cfrhfffD353rl8Pb70ljbFPG8OAhFKSFmzL8krA\nyA7aREfK73ZgqXwqPPKYBHnGj5XHDh2E6wdJ8+Whd8Kc+XD3vbnL0cLpdhkkJGRviG2LCKR/b/hT\ngjeDBueeGJaTZcnUs0aNJX18SaBELa8vfGcg0LJjj9wl3HtAjmsYEszatDFYmub3g8uRvbl4Tr5A\n3b3XDw0bAbD8u0/pPnswlWJS+aHTGJx/JnF500AWUZky4HbicEgZ4vz5yOIzOUUih6F27JCfFSrI\neecM2hiGLHaKupDO8sp/B/ndSfN4gtldiYnB66aUUkqVNJfztGTt1ChdnR/7f0u1+Cp03P0ifreL\nDpnfMG0arFkb3G7OHNi4SYashWVPWrMDRuG+H3WKWnj252gYgJX9RiYEAzj2NTWM7BNp7bXSyaBR\nIBOtYkWsrVt55IenefS7xxlYuy/vOXoCUKbfpbI70wSPi+QUg/btJdOfiIjgOfhNucGq651C05ws\npZQ6Q9xONyOvHkm52HK88uMrpB1LY8yEzxjQN5I335TvwZUr4eWXpWzttIqNzp6dYiEBBJthSEPt\ntP3BO2cDr4PJk+CF5yQw9OhDsHMnvPomXNOn4GOapgR2oiLky/mafjByBOzdk7upNcAnH0vQYsCg\n/PdrB4ycDnBFSNBmyeKCz8fjkv4D23bLQtRuvL1gvvzs0El++kwoUxoOHAmO0c15fJ9Pgm6HjkKd\nuvjdTr6b9S4Nrm3AzM6fkxRRGg4cZqdvk7wmKelksGbLFokh4XJCufKw6Ifs+14wT34vl5r3uHuP\nB05kFP6umP25J8Tnv11kyAS10omaqq2UUurscQUCNJxibz17dLtpkhqZzIKrp9Fz5nXMqfQDzeaN\n4dG3XmLYMKhaBY4fh2PH4I3Xc1f5Z2MY+fe+cYSUqGmmblC24J8hn2voGsMb6MtpczgCQ1qi5O9d\ngaxsuzzN6QS/D7NSRTb/vpB//zyFOxvcyn87/BvHkMEcLl2FP83qdIZAk2s3lhWyBrODRHYZXF7r\nLRWW/petlFJnkMNw8O8u/+a1rq8xfvV47l12GT8sP8wnn8Bjj8mX2a23noEDO53S9yjLJ//iY3Mv\nekrFyBeoncHicMBL/4aMEzCgLxxNh1FjCxcwsixZEERGBHslDRwkjz//bO605CNHYMI4uLInlC2b\n/34zAhkzifGS8dOiFaxaCenpBZ9XhEeCNaELlfnzoHIVqFYt+FhcDCQnhG8g7vMH+hElYFomj616\njZ/K+um6L5653caSFJkAhkH5qm6qOiVl2kosA243S5bAxx/DDTcg1zclRc776FGp8b//Xhg3Bq6/\nUZps57UwjXAX7e5rpk96XhW0KPLkKE9zn+JCXSmllCoup1NKmgpi/x9/n1++t70+WYP4/PI9FhcD\nCaUoHZPErF5fsb11PRK37uWng/cybZrF7bfDI/+EryZBvXpFPEfLgptvgrf/K3/bmTSFKVH7O5Wy\n+f3BSIMzTDZ3li/7jTBHYD1qr3V2p8nPlBR53OXkUOZhZnhXE5N2gBdaPc7b7f+Nw7Lg+wVw6SVM\nmGDwxxrAAtPh4u23ZeZJu3YESvJDGmLr0I8i0aCRUkqVgPtb38/nvT5n4daFtP24Dcm1N9O1K8Tl\nVUd/OpSOk+kSliUBl5ycTtkmNB24Rk148hm4uA1MmgZNmxXuWFk+aa6dkhQMQlWrDv94UJpojx6V\nfftxY+Q23/X51OVZlvQRio+R/UZHyV2plq1kMfLT8oLPy8gxDSwzE35cKKVpRqB+3uWU4EmpWAmy\n+HL0gvL7ISWJTMvH4OUP8eJv/+NYvVo02OEn1hl1clOHy8FFFQ4AMHVRGW4e6uLqq+HDD6FWrcC5\n2KVgf66Hm66HSRPhgYfh6efkukXkETTyeArfINSygDw+85xcLqhZU34vXx5cOklEKaXUWeJ0ZM8+\nycm0ZL3h88l2bpf0doyNlu/w0nEQGxPMKnG7iHR4uP7eTwDYPGEEN825kQZNMmjU8BRb2nzzDYwb\nC//9TzDAUdgStcwsmbr6d+AzwQhcYIdD1lt2eZhpSpNsw4AHH4CF3wdeFFLGZg8NSZFM9W3HdtJ2\n/GUsde0h5Rg8fuEw+U/l55/gyBHie17Cww/DA/8wuel2BzVqOxg5EqZODUkAi/AEsozCtAJQ+dKr\npZRSJWRQg0HMum4WO47uoMUHLVi0bdGZPWBkhPT/iYvJO/e6dBxgZc8Eum4IfDEGKlYs3HHsuvTy\nZaRXkjOk2eAdw6BdB3j2KfhjdWB7P3w6Epo1h/oNwu/TDhjFRkG5MsGpaABNmsoxloYpUctZM5/T\njwslWNWho/zt8wczrhwOSE6UvkX29cjyQak4Dhkn6P5Fd0Zt/Ir/q/8AHbsOxUg/Kr2RQsRm7Mdy\nOml7RQL33O9kyxbo2TNkAztodNMQWLJIJtDddU+wrj6vzCC3k/xX0iGyfPKeCjNK1u2EJs1h+jdw\nUcNgo3CllFKqpDkc2UvrIZidkxUYRhEdCfGlpHt1bLSUxHvc8v2ZMxDgd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ZlSElccWb7s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\nzfAPLh0xjcifUAEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11754d400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train, y_train = create_toy_data_3d(sinusoidal, n=20, std=0.1)\n",
    "x0 = np.linspace(0, 1, 100)\n",
    "x1 = x0 + np.random.normal(scale=0.1, size=100)\n",
    "x2 = np.random.normal(scale=0.1, size=100)\n",
    "x = np.vstack((x0, x1, x2)).T\n",
    "\n",
    "model = GaussianProcessRegressor(kernel=RBF(np.array([1., 1., 1., 1.])), beta=100)\n",
    "model.fit(x_train, y_train)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(model.kernel.params))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.5, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "\n",
    "model.fit(x_train, y_train, iter_max=100, learning_rate=0.001)\n",
    "y, y_std = model.predict(x, with_error=True)\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train[:, 0], y_train, facecolor=\"none\", edgecolor=\"b\", label=\"training\")\n",
    "plt.plot(x[:, 0], sinusoidal(x[:, 0]), color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x[:, 0], y, color=\"r\", label=\"gpr {}\".format(np.round(model.kernel.params, 2)))\n",
    "plt.fill_between(x[:, 0], y - y_std, y + y_std, color=\"pink\", alpha=0.2, label=\"gpr std.\")\n",
    "plt.legend()\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 6.4.5 Gaussian processes for classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1r1RN+5pxuV2tExLGGwLOWEJVls9fzdzHFrJ5VSPLXl3Jyn+s4YqbL+H6X1zL\nEVPHUhOL89xvXsYz6XBtKDVYho4bjL82f9fALvn8DLyBtt02vAEfM687n/FjB7feNYXs7oI++b/P\nsOmF7URCEcKHnJrn5jVbmPvwA6T/6IXQ0NzMBxQf+M/G6Zyayo/UXN5leUzlqbgamLiEa/7zo2xY\n0cj8V5YzMDqYaReeULS578dOHk0s0cxLhph3ImifGuKqrYGkcSUSjPDHHz3BfzxxM+uXbeKOz/+a\nSCSKxuJtvu4ujxuP180nvvkveS3rxJPGc/3Pr+GJ259h67vb6TOogQ9/bjqnX9x2nrrkSt5dLcH2\n+v+9RTQSxYsT3K6DQWKRGMvnv8v0j2SoSXWx6o/UzUI1CuHXcMY9AjX/5kxlbapOXgKsq9VGep0I\n46aMhn61RR9GVNMQ4MP/fgH/d+9LRIKJJtMmD5FIDM+Etgt0uA4G2bNtH8HmIH/40eOEgx1vRtT2\nreXUi07kg1eeyaAC3OU76pSJ3Prgl7vcL5sQi6YEd+q8/etW+kBqQNtPOe1HAu1ml2hPvEjDDRD/\ntHNNzD3UqZmZqpRzEzJltZGLgMnAx0Rkcq7HrSTnX3021/30ao4982jGTB7FRZ+dTr+hfZ3+Xmtp\n07zUhho2bdvHlu37W5ubrc1OIByM8G83XVKQ8OqurrpJHH2ac10vKd4QABEmnjgB6fMdoA8QSPx4\nIHAp+KZmOFo7rgbwjLbwqnL5qIEVZLWRSnP0aZPadKT113h58q7nW2tlkbXg9Xk48cITGVM7Dt3k\nIRJqe0fOOzGAp09tm+4JpTCEJ1Mt7N9uvpT1y+4kHAoTWRuhZrIHf704U0B7BiMDfg2RZaBN4Jni\nDP8xphvyEWBZrTYiIrOAWQAjRluv6bOvOJMdm3cz/4nX8fo9RMNRjj7tSK645VLEJZx+8TQWPL2I\nSDilm0Sjlw9c84E2YZHsNNqVQgVdsimZzqARA/je4zfz2tOL2LxqC/1PqeP4syczbFxilSPxgO/E\ngpTLVIdeu4ifWGJpNsBxJx1f8A5ZpT4Lq7iEK26+lA99bjrbN+xkwPB+9B96uCvA5V+Zyf6dB1j1\njzV4fB4ioSgnT5/Khdec0+Y42b7HQvaO70xtnxqmX3VW6+OCjuE0VScfAdblaiMms/p+ddSf0PHO\nm8fn4d9/ejV7t+1jZ+Nuho4bQt9B3VusNlVyaFO3xirGtqHBFyG+G/GdAL4zc1qgI6kkZ68wZSkf\nAdblaiO616cwAAAPNUlEQVSm5/oP60f/YfnppNmtEAu/iR78HyAGxNDw6+B+Cunzoy4nQsymDMbk\nQ853ITOtNpLrcU1hZDVOUWPowV/g9JRPjoEMOovjBp9p3W3ruu3Mf3IR65ZsIB7rZAxXGjb1jsmH\nvFwDU9VngGe63NGUhC5rQbFNOGsqtheB8Dzi/su4/1sPs2zuSkDQhhqe2f53vnrvdc5UP7me35gs\nVdxQIpOd5EwZaYmPjGMOJcD8JxaybO4qIsEIkWCYcDDEgV0HuPeW33erDFYLM7mq2AAbN2qg/ZXv\nQmqIHTrQwku/f5V7b/k9f713BTFN1yfLjwQuYu5jC1v7r8UbAkTWOoPlt2/Ywd5t+7I+tzG5qrix\nkKZ7hntGsmzJan77nT8R23OQSDDC8nmrWTqngVvuaMHtDiX2jDkDqX3vJxLOsECsy9W231oW597Q\nuMXuSJoeq9gamMne3DvepKU5SMjrDI6OhqNsWQs/vekEpOEWpP5zSL/bkfrrQISTL5iKx+9pM44T\noK5PDUNGD+r2+a0paXqqogMs2Yy0pmTnVr62hvA7zl3E1FDa8s42QrHJ4P8guIe1bp9+1Vn0GT8M\nr99HZC14vB58AR/X/tfHO507Px1rSppcVHwTMtk8yWbITbV+mbx+D8Hmw7NGJEPMHYzg9nT8G7dt\nbxPXfP+jbPv7HlYvXsvA4f054+Jp9BvSt8dlsM6tpicqPsCSsvly9EbIbd+4k40rGuk/rC8TTxiP\nuLpZZSmA93/kNF568FUioUjrzBj+ozxMOHsSjdudWVjbj3kcVTOGUTPGtFknsqesW4XpqaoJsGx0\nFXJtFqNNo7Nwi8fj/O7bf+LtOctxuZ1rTX0GNnDjr2blVHPJhxmfOZfGNe+xetFa3G438Xicoa4h\nfOozV1HjCbT23ofC1lKtFma6ywKsGzr7cmUKt+QX/tVHF/D2qysTd+mcO3W73ovwm9v+wFfvvb4g\n5c2Wx+vhup9fw7b1O9jyz60MGjWQsceMar2e1RtNa6uFmZ6wAMuTTOGWbJbOXTgXRoXxcngCQ43H\n2biikYN7moo25XWqYeOHMGz8kKKd37pVmO6yACuw1i/j/kNtFq5N8vicFYqMMd1X0d0oSskJ507B\n43XjOhhs81Pbp5bQoGZrPiV0OsTJmHYswHrJRZ85j75D+uKrceZw93jd+Gp8fO6b/8K40YeXKrMg\nc1iImWxYE7KX1PWt5baHv8KiZ97in2++y6CRA3j/v5xK/2HOmMPD/dXsi2sX9E22LMB6kb/Gx/v/\n9TTe/68dlgxo5fS36ny9RWOMw5qQJaraayB2LcxkwwKsBFk3AmOyYwFmSlK110BNduwaWAnLtGBs\nKYmGozz3m5d57alFRKMxpp5zLJd+/kLq++feMddqoqYrFmAlqrMFYwtF48r2jTvx+r0MHJHdKtm/\nvPF+3l26sXUV8YV/fYNVC97hO3++CV+g+0uwWc3LdIcFWInSuNL4znts376XCVPHFXyo0ZpFa/nt\ntx8m2BxC43GGjB3MrJ9c3ekiHRtXNvLusk2t4QUQi8Zo3neIN154mzMumdbpOTOFldW8TLYswErQ\nri17uOPz97I/HCW23kU0EmX6VWdx8fUXFuR8e7ft456v/o5wYp57gPfWbuPns+7h+3+5FZcr/aXS\nVVtW4pkQh1Db7UqY1VtXMS46vNPzWlAVRjXdvbUAKzWq3H3j/ezeupd4nZ9Is7P55T/MY9yxYzju\nrGPyfsr5T75OLNp2XUdVJdgUYuHbCxl33Ji0r+s7uA/elgjx5rYJ5gl4mXjEUAuoIqim8AILsJKz\nbf0O9mzdB3HFdTCId6Kz6k84GObvj8zPW4ClNt+2xt7DNS7a4Za0yx8jEI1lDKKxIwYwZ/aL7A5F\niKcEoMfj4vSLT85LOU32emPOtlJjAVZiWppDuDxtZ2n1TnSm4Gk+0NJh/1wueieD6ZTTj2TdnBWE\nW8JtnpdwlCOOH5vx9eISvnrvdTzw3UdYs3gdACMmDOWT372C+n51PS6X6b5qDC+wACs5o48a0WZN\n2eQUPDWTPRz1kbEdAisfzbSTzz+eF383h51bdhNNTO3jC/g44bwpDBk7uNPX9hnYwBfv/AyhljAa\nixGor8m5PCY77ZuL1RZeYAFWcjw+Dx/75r/y4Pf/TDQSQ2NxApE4AwbVctnVZ+Ov9RfknDfd/wX+\n9tCrvPniUrx+H2ddfnqXdxFT+ROzbJjeUa01rvYswErQtAunMmz8EOY++g/27zzAsWcezWkzT+5R\nv6psBer8fHjW+Xx41vkFO4fJDwuvwyzASkxrs6DWxxlXn2138kwbFl5tWYCViNTrGckPp/VKN6ks\nvDqyACsBnX0wbamx6mYX6jtnAVZE6WpdqWxm0upmNa6uWYAViX04TWfs85Edmw+sCOzDaTpjn4/s\n5VQDE5GfABcDYWAdcK2q7uvqdeFwda6D2FWT0RgLr+7JtQb2IjBFVY8H3gG+ke0Lq23QaeoHs9w/\nnFv+uZU5D89n8XNvEQ5Gun6ByYqFV/flVANT1RdSHi4ALs/mdV5xOmSmhlil3mmrpFqXxpXffe8R\nlry8DFXF7XHzxx8/yQ13f44xx4wqdvHKmoVXz+TzGtingWczPSkis0RksYgs3rtnd2tNJPkPVsk1\nskqodQG88cIS3n5lOZFghGgoSqg5RLApyK++9gAa164PYNKy8Oq5LmtgIvISMCzNU7ep6lOJfW4D\nosBDmY6jqrOB2QBTjpva5tOe7C5QSX2eKvFDOe/JRW1mrIg3BABoiiuvv7aaoeOGdHmMSvn3zZdK\n/Jz0pi4DTFWnd/a8iFwDzATOU9Ue/xmupD5PlfqhjEViraEFzhQ/AO5aF/2Cg7J6vxsaO/4bV1uo\nWefU/Mn1LuQM4BbgbFU9lJ8ila9Kut6VKvm+Jpw9mQ1bdtOyou2Fe5fHxZhjsnu/7X8vyZp3qkoO\ntEr941YsuXZkvRPwAy+KCMACVb0ulwOWazOyUj+Yqe9ryLnDeOeJTWyo2Uy4JYTX5wGXi8/86BO4\n3D27nJp++FT+5zwrBZX6GSmmXO9CTsxXQaB8r4VV4gcz3Xtye9x8+a7PsnLBO6xZtJaG/vWc+qGT\n6DuoIa/nTj1npdTQKvEzUgpKbihROYVYJTYZu/qiiUs49n1Hcez7juqV8lRCDc3Cq3BKLsCgPEKs\n0j6U5RTG7ctXyoFWaZ+TUlOSAQalfVeykj6U5RRcmXTV5ITeDTW7y9h7SjbASlUlhlclvJekdO+l\nfagVMswq8XdayizAslSsD+Zwz0g2NG7J65euEmpd3dFbNTQLr95X0gFWiC9vT2xo3F0xH8pq/5IV\nqoZW7b/XYinpAIPihlgljc+0L1hmudbQ7HdbPCUfYFCcEKukD2Ul1SALLdPvKXmns/1nsJI+J+Wo\nLAIMejfEKuVDWSnvoxQcnjWl451x+/0WT1lNKe2EWGGbdZXwpd/QuLsi3kcpaj81kv1+i6tsamBJ\nhaqJVcqdOQuu3mG/39JQdgEG+Q+xcvjSdzUqoRzegzH5VlZNyFT5ak4mL3CX8he/s7JZc9FUs7Ks\ngSXlUhMrxy4SqbWwSmnyGpOLsg4w6FmIlWONJXWAe+o2Y6pZ2QcYZB9i5f7lL8cyG1NIZXsNrL1s\nr4mV+vUuY0z2KibAIHOIJS90W3AZU1kqogmZKtmcTLfdGFNZKi7AwMLKmGpRUU1IY0x1sQAzxpQt\nCzBjTNmyADPGlC0LMGNM2bIAM8aULQswY0zZsgAzxpQtCzBjTNmyADPGlC0LMGNM2bIAM8aULQsw\nY0zZsgAzxpQtCzBjTNnKS4CJyNdEREVkUD6OZ4ypPCIyQ0TWiMhaEbk1zfMiIncknl8qIid1dcyc\nA0xERgMXAJtyPZYxpjKJiBu4C7gImAx8TEQmt9vtImBS4mcWcHdXx81HDeznwC2A5uFYxpjKdCqw\nVlXfVdUw8DBwabt9LgUeUMcCoJ+IDO/soDlNKS0ilwJbVPVtEelq31k4qQoQOmbi8OW5nLsXDQJ2\nFbsQ3VBO5S2nskJ5lfeoXA+wYvnS54+ZODzby0IBEVmc8ni2qs5OeTwS2JzyuBE4rd0x0u0zEtia\n6aRdBpiIvAQMS/PUbcA3cZqPXUq8mdmJYy5W1WnZvK7YyqmsUF7lLaeyQnmVt12Y9IiqzshHWQqp\nywBT1enptovIccB4IFn7GgW8KSKnquq2vJbSGFPutgCjUx6PSmzr7j5t9PgamKouU9UhqjpOVcfh\nVPdOsvAyxqSxCJgkIuNFxAdcCTzdbp+ngasTdyNPB/arasbmIxRvWbXZXe9SMsqprFBe5S2nskJ5\nlbekyqqqURH5IvA84AZ+o6orROS6xPP3AM8AHwLWAoeAa7s6rqjazUNjTHmynvjGmLJlAWaMKVtF\nD7ByGIYkIj8RkdWJ4Q1PiEi/Ypepva6GaZQSERktIq+IyEoRWSEiNxS7TF0REbeIvCUify12Wboi\nIv1E5NHEZ3aViJxR7DIVSlEDrIyGIb0ITFHV44F3gG8UuTxtZDlMo5REga+p6mTgdOALJV5egBuA\nVcUuRJZuB55T1aOBqZRPubut2DWwshiGpKovqGo08XABTv+UUpLNMI2SoapbVfXNxP8fxPmCjSxu\nqTITkVHAh4FfF7ssXRGRvsBZwH0AqhpW1X3FLVXhFC3AUochFasMPfRp4NliF6KdTEMwSp6IjANO\nBBYWtySd+gXOH9p4sQuShfHATuD+RJP31yJSV+xCFUpB+4HlaxhSb+isrKr6VGKf23CaPw/1Ztkq\nlYjUA48BN6rqgWKXJx0RmQnsUNU3ROScYpcnCx7gJOBLqrpQRG4HbgW+XdxiFUZBA6ychiFlKmuS\niFwDzATO09LrPNftIRjFJiJenPB6SFUfL3Z5OnEmcImIfAgIAH1E5EFVvarI5cqkEWhU1WSN9lGc\nAKtIJdGRVUQ2ANNUtSRH+ovIDOD/AWer6s5il6c9EfHg3Fw4Dye4FgEfV9UVRS1YBuL81fodsEdV\nbyx2ebKVqIHdpKozi12WzojIXOCzqrpGRL4H1KnqzUUuVkEUayhRubkT8AMvJmqMC1T1uuIW6bBM\nwzSKXKzOnAl8ElgmIksS276pqs8UsUyV5EvAQ4kxh++SxZCcclUSNTBjjOmJYnejMMaYHrMAM8aU\nLQswY0zZsgAzxpQtCzBjTNmyADPGlC0LMGNM2fr/xOlJ9cWAjisAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1179f66d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_toy_data():\n",
    "    x0 = np.random.normal(size=50).reshape(-1, 2)\n",
    "    x1 = np.random.normal(size=50).reshape(-1, 2) + 2.\n",
    "    return np.concatenate([x0, x1]), np.concatenate([np.zeros(25), np.ones(25)]).astype(np.int)[:, None]\n",
    "\n",
    "x_train, y_train = create_toy_data()\n",
    "x0, x1 = np.meshgrid(np.linspace(-4, 6, 100), np.linspace(-4, 6, 100))\n",
    "x = np.array([x0, x1]).reshape(2, -1).T\n",
    "\n",
    "model = GaussianProcessClassifier(RBF(np.array([1., 7., 7.])))\n",
    "model.fit(x_train, y_train)\n",
    "y = model.predict(x)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "plt.contourf(x0, x1, y.reshape(100, 100), levels=np.linspace(0,1,3), alpha=0.2)\n",
    "plt.colorbar()\n",
    "plt.xlim(-4, 6)\n",
    "plt.ylim(-4, 6)\n",
    "plt.gca().set_aspect('equal', adjustable='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
